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JAMB 2016

2016 JAMB Physics Past Questions

The 2016 JAMB Physics past questions with answers: 48 objective questions from the 2016 paper in the DeeepSolve question bank, each with its answer behind "Show answer". Try each question before you check, then practise the paper as a timed JAMB-style CBT.

Past questions © the examination body (JAMB/WAEC/NECO). DeeepSolve is not affiliated with them. Rights holders: see /copyright.

Questions

  1. 1.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.

  2. 2.

    Which of the following waves is both transverse and mechanical?

    1. A.Water waves
    2. B.Radio waves
    3. C.Sound waves
    4. D.X-rays
    Show answer

    Answer: A. Water waves

    AI explanation

    Analysis

    To solve this, we need to understand two key classifications of waves:

    1. Mechanical Waves: These require a material medium (solid, liquid, or gas) to travel. They cannot travel through a vacuum.
    2. Transverse Waves: These are waves where the particles of the medium vibrate perpendicularly (at 90 degrees) to the direction of wave propagation.
    Concept Explanation
    • Mechanical vs. Electromagnetic: Sound waves and water waves are mechanical. Radio waves and X-rays are electromagnetic waves (they do not require a medium and can travel through a vacuum).
    • Transverse vs. Longitudinal: • Transverse: Particles move up and down (perpendicular) as the wave moves forward. Examples include waves on a string and water waves. • Longitudinal: Particles move back and forth (parallel) in the same direction as the wave. Sound waves are the classic example of longitudinal waves.
    Step-by-Step Solution
    1. Evaluate Radio waves and X-rays: These are electromagnetic waves. Since they do not require a medium, they are not mechanical. We eliminate options B and D.
    2. Evaluate Sound waves: Sound waves are mechanical, but they are longitudinal because the air particles vibrate parallel to the direction of the sound. We eliminate option C.
    3. Evaluate Water waves: Water waves require a medium (water) to travel, making them mechanical. As the wave moves across the surface, the water particles move up and down (perpendicular to the direction of the wave), making them transverse.
    Conclusion

    Water waves satisfy both conditions: they are mechanical (need water) and transverse (particles move perpendicularly).

    Exam Tip: Remember the acronym "EM-L" for Electromagnetic waves (Radio, X-rays, Light, etc.)—they are all transverse but not mechanical. Sound is the only common mechanical wave that is longitudinal. Everything else mechanical (like ripples on a pond or waves on a string) is transverse.

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  3. 3.

    Which of the following electromagnetic waves has the shortest wavelength?

    1. A.Visible Light
    2. B.Ultraviolet rays
    3. C.Infrared rays
    4. D.Gamma rays
    Show answer

    Answer: D. Gamma rays

    AI explanation

    Analysis

    The question asks you to identify which of the listed electromagnetic waves has the shortest wavelength. To solve this, we must recall the electromagnetic spectrum and the relationship between wavelength, frequency, and energy.

    Concept: The Electromagnetic Spectrum

    Electromagnetic waves are arranged in a spectrum based on their frequency and wavelength. The relationship is governed by the wave equation:

    c=fλc = f \lambda

    Where:

    • cc is the speed of light (constant).
    • ff is the frequency.
    • λ\lambda (lambda) is the wavelength.

    Because the speed of light is constant, frequency and wavelength are inversely proportional. This means:

    • Waves with high frequency have short wavelengths.
    • Waves with low frequency have long wavelengths.

    The order of the electromagnetic spectrum (from longest wavelength/lowest frequency to shortest wavelength/highest frequency) is:

    1. Radio waves
    2. Microwaves
    3. Infrared rays
    4. Visible light
    5. Ultraviolet rays
    6. X-rays
    7. Gamma rays
    Step-by-Step Solution
    1. Compare the options: • Infrared rays: Located near the low-frequency end of the spectrum (long wavelength). • Visible light: Located in the middle of the spectrum. • Ultraviolet rays: Higher frequency than visible light (shorter wavelength). • Gamma rays: Located at the extreme high-frequency end of the spectrum.
    2. Apply the principle: Since Gamma rays have the highest frequency among all electromagnetic waves, they must mathematically possess the shortest wavelength.
    3. Conclusion: Comparing the options provided, Gamma rays are the most energetic and have the smallest wavelength.
    Exam Tip

    Remember the mnemonic "Raging Martians Invaded Venus Using X-ray Guns" to recall the order of the spectrum:

    • Radio
    • Microwaves
    • Infrared
    • Visible
    • Ultraviolet
    • X-rays
    • Gamma rays

    As you move from left to right in this mnemonic, the frequency increases and the wavelength decreases!

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  4. 4.

    Boiling occurs when the vapour pressure of a liquid is

    1. A.At the evaporation point
    2. B.Less than the atmospheric pressure
    3. C.Greater than the atmospheric pressure
    4. D.Equal to the atmospheric pressure
    Show answer

    Answer: D. Equal to the atmospheric pressure

    AI explanation

    Analysis

    The question asks for the specific physical condition that must be met for a liquid to reach its boiling point.

    Concept Explanation

    Boiling is a phase transition from liquid to gas that occurs throughout the entire volume of the liquid. For bubbles of vapour to form and rise within the liquid, the internal pressure of the vapour must be strong enough to push back against the surrounding atmospheric pressure (or external pressure) pushing down on the surface of the liquid.

    • Evaporation: This occurs only at the surface of a liquid at any temperature.
    • Boiling: This occurs when the vapour pressure of the liquid becomes equal to the external atmospheric pressure. If the vapour pressure is lower than the atmospheric pressure, the bubbles will collapse before they can reach the surface.
    Step-by-Step Solution
    1. Define Vapour Pressure: This is the pressure exerted by the vapour molecules in equilibrium with the liquid at a given temperature.
    2. Define Atmospheric Pressure: This is the pressure exerted by the weight of the atmosphere above the liquid.
    3. The Condition for Boiling: As a liquid is heated, its vapour pressure increases. Boiling begins the moment the vapour pressure rises to match the atmospheric pressure. At this point, the liquid can no longer contain the vapour, and bubbles form freely throughout the liquid.
    4. Conclusion: If the vapour pressure were less than the atmospheric pressure, the liquid would not boil. If it were greater, the liquid would have already reached its boiling point and surpassed it. Therefore, the exact point of boiling is defined by equality.
    Identification of Answer

    The correct option is D.

    Exam Tip

    Remember the "Pressure Balance" rule: Boiling = Vapour Pressure equals Atmospheric Pressure. If you are asked about boiling at high altitudes (like on a mountain), remember that atmospheric pressure is lower there, which is why water boils at a temperature lower than 100°C!

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  5. 5.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.

  6. 6.

    What will happen to the pressure of a gas if its temperature is reduced to -273oC?

    1. A.It will decrease
    2. B.it will drop to zero
    3. C.It will increase
    4. D.It will remain constant
    Show answer

    Answer: B. it will drop to zero

    AI explanation

    Analysis

    The question asks for the effect of reducing the temperature of a gas to −273∘C-273^\circ\text{C} on its pressure. This relates to the Pressure Law (or Gay-Lussac's Law) and the concept of Absolute Zero.

    Concept

    The Pressure Law states that for a fixed mass of gas at a constant volume, the pressure (PP) is directly proportional to its absolute temperature (TT) measured in Kelvin:

    P∝TorPT=kP \propto T \quad \text{or} \quad \frac{P}{T} = k

    To convert temperature from Celsius (∘C^\circ\text{C}) to Kelvin (KK), we use the formula:

    T(K)=t(∘C)+273T(K) = t(^\circ\text{C}) + 273
    Solution
    1. Convert the given temperature to Kelvin: Given t=−273∘Ct = -273^\circ\text{C} $T=−273+273=0 KT = -273 + 273 = 0\text{ K}$
    1. Apply the Pressure Law: Since P∝TP \propto T, if the temperature TT becomes 0 K0\text{ K} (Absolute Zero), the pressure PP must also become zero. $P=k×0=0P = k \times 0 = 0$

    At −273∘C-273^\circ\text{C} (Absolute Zero), the kinetic energy of the gas molecules theoretically becomes zero, meaning they stop moving and exert no force (pressure) on the walls of the container.

    Conclusion

    When the temperature of a gas is reduced to −273∘C-273^\circ\text{C}, its pressure drops to zero.

    Exam Tip

    Always remember that in gas law calculations, you must convert Celsius to Kelvin. If you see −273∘C-273^\circ\text{C} in a physics question, immediately associate it with "Absolute Zero" and "Zero Pressure."

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  7. 7.

    A saturated vapour pressure of a liquid increases when the

    1. A.Temperature of a liquid increases
    2. B.Volume of the liquid increases
    3. C.Volume of the liquid decreases
    4. D.Temperature of the liquid decreases
    Show answer

    Answer: A. Temperature of a liquid increases

    AI explanation

    Analysis of the Question

    The question asks about the relationship between the Saturated Vapour Pressure (SVP) of a liquid and other physical factors. We need to identify which factor causes the SVP to rise.

    Concept Explanation

    Saturated Vapour Pressure (SVP) is the pressure exerted by a vapour when it is in dynamic equilibrium with its own liquid in a closed container.

    1. Kinetic Theory: Molecules in a liquid are in constant motion. Some molecules near the surface have enough kinetic energy to escape into the space above the liquid (evaporation).
    2. Temperature Effect: Temperature is a measure of the average kinetic energy of the molecules. When you increase the temperature, more molecules gain sufficient energy to overcome the intermolecular forces holding them in the liquid phase.
    3. Equilibrium: As more molecules escape into the vapour phase, the pressure exerted by the vapour increases until a new equilibrium is reached at a higher pressure. Therefore, SVP is strictly a function of temperature.
    4. Volume Independence: Changing the volume of the container or the volume of the liquid does not change the SVP. If you increase the volume of the container, more liquid will simply evaporate until the pressure returns to the original SVP for that specific temperature.
    Step-by-Step Solution
    • Step 1: Recognize that SVP is defined as the pressure of the vapour in equilibrium with the liquid at a specific temperature.
    • Step 2: Recall the kinetic theory of matter: higher temperature = higher average kinetic energy = more molecules escaping the liquid surface.
    • Step 3: Evaluate the options: • Option A: Increasing temperature increases the kinetic energy of molecules, leading to a higher rate of evaporation and thus a higher SVP. This is correct. • Option B & C: Changing the volume of the liquid or the container does not change the equilibrium pressure (SVP) at a constant temperature. • Option D: Decreasing the temperature reduces the kinetic energy of the molecules, which decreases the SVP.
    Conclusion

    The saturated vapour pressure of a liquid is directly dependent on temperature. As the temperature of the liquid increases, the saturated vapour pressure also increases.

    Exam Tip: Always remember the phrase "SVP depends only on Temperature." If you see a question asking what affects SVP, ignore volume, surface area, or pressure changes—look for the temperature option!

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  8. 8.

    A manometer is an instrument used for measuring

    1. A.Relative density of liquid
    2. B.Pressure in liquids and gases
    3. C.Humidity
    4. D.Atmospheric pressure
    Show answer

    Answer: B. Pressure in liquids and gases

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  9. 9.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.

  10. 10.

    Which of the following statements about wave motion is correct?

    1. A.Electromagnetic waves are transverse
    2. B.Transverse waves do not require a medium for propagation
    3. C.Longitudinal waves vibrate perpendicular to the direction of travel
    4. D.All mechanical waves are longitudinal
    Show answer

    Answer: A. Electromagnetic waves are transverse

    AI explanation

    Analysis of the Question

    This question tests your understanding of the fundamental classification of waves: Mechanical vs. Electromagnetic and Transverse vs. Longitudinal. To solve this, we must evaluate each statement based on the physical properties of waves.

    Concept Explanation
    1. Electromagnetic Waves: These are waves that do not require a material medium to travel (they can travel through a vacuum). They are always transverse in nature because their electric and magnetic field oscillations occur perpendicular to the direction of energy propagation.
    2. Transverse Waves: Waves where the particles of the medium (or the field) vibrate perpendicularly to the direction of wave travel (e.g., water waves, light waves).
    3. Longitudinal Waves: Waves where the particles of the medium vibrate parallel to the direction of wave travel (e.g., sound waves).
    4. Mechanical Waves: These require a material medium to propagate. They can be either longitudinal (like sound) or transverse (like waves on a stretched string).
    Step-by-Step Evaluation
    • Option A: Electromagnetic waves are transverse. This is correct. Light, X-rays, and radio waves are all electromagnetic and are classified as transverse waves.
    • Option B: Transverse waves do not require a medium for propagation. This is incorrect. While electromagnetic waves (which are transverse) don't need a medium, mechanical transverse waves (like waves on a guitar string) do require a medium.
    • Option C: Longitudinal waves vibrate perpendicular to the direction of travel. This is incorrect. By definition, longitudinal waves vibrate parallel to the direction of travel.
    • Option D: All mechanical waves are longitudinal. This is incorrect. Mechanical waves can be transverse (e.g., waves on a rope) or longitudinal (e.g., sound waves in air).
    Conclusion

    Based on the analysis, Option A is the only scientifically accurate statement.

    Exam Tip

    Remember the mnemonic "L-P" for Longitudinal = Parallel, and "T-P" for Transverse = Perpendicular. This simple trick will help you avoid mixing up the direction of vibration in your exams!

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  11. 11.

    A charged particle is moving in a uniform magnetic field. if the direction of motion of the charged particle is parallel to the magnetic field, the path of the charge will

    1. A.Be a straight line
    2. B.Curve inwards
    3. C.Be a parabola
    4. D.Curve outwards
    Show answer

    Answer: A. Be a straight line

    AI explanation

    1. Analyze the question

    The question asks for the trajectory (path) of a charged particle when it moves through a uniform magnetic field, specifically when its velocity vector is parallel to the magnetic field lines.

    2. Explain the concept

    The force (FF) exerted on a charged particle moving in a magnetic field is given by the Lorentz force formula:

    F=qvBsin⁡(θ)F = qvB \sin(\theta)

    Where:

    • qq = charge of the particle
    • vv = velocity of the particle
    • BB = magnetic field strength
    • θ\theta = the angle between the velocity vector (vv) and the magnetic field vector (BB)

    When the motion is parallel to the magnetic field, the angle θ=0∘\theta = 0^\circ. Since sin⁡(0∘)=0\sin(0^\circ) = 0, the force FF becomes:

    F=qvB(0)=0F = qvB(0) = 0

    Because there is no magnetic force acting on the particle, it experiences no acceleration or change in direction. According to Newton’s First Law of Motion, an object in motion will continue in a straight line unless acted upon by an external force.

    3. Show the solution
    • Step 1: Identify the angle between the velocity and the magnetic field. Since they are parallel, θ=0∘\theta = 0^\circ.
    • Step 2: Apply the magnetic force formula F=qvBsin⁡(θ)F = qvB \sin(\theta).
    • Step 3: Calculate the force: F=qvBsin⁡(0∘)=0F = qvB \sin(0^\circ) = 0.
    • Step 4: Conclude the effect on motion. With zero net force, the particle maintains its constant velocity and direction. Therefore, it moves in a straight line.
    4. Identify the answer

    The correct option is A.

    5. Exam Tip

    Remember the "Sine Rule" for magnetic force:

    • If θ=0∘\theta = 0^\circ or 180∘180^\circ (parallel/anti-parallel), sin⁡(θ)=0\sin(\theta) = 0, so no force (straight line).
    • If θ=90∘\theta = 90^\circ (perpendicular), sin⁡(θ)=1\sin(\theta) = 1, so maximum force (circular path).
    • If the angle is between 0∘0^\circ and 90∘90^\circ, the path is a helix (a spiral).

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  12. 12.

    A metre rule is pivoted at its mid-point with a vertical force of 10N hanging from the distance 30cm from the mid-point. At what distance must a 15N force hang to balance the ruler horizontally?

    1. A.30cm
    2. B.10cm
    3. C.20cm
    4. D.25m
    Show answer

    Answer: C. 20cm

    AI explanation

    1. Analyze the question

    We are dealing with the Principle of Moments. A metre rule is balanced at its pivot (the mid-point). For the rule to remain horizontal, the clockwise moment must equal the anticlockwise moment.

    • Pivot: Mid-point
    • Force 1 (F1F_1): 10N at a distance (d1d_1) of 30cm from the pivot.
    • Force 2 (F2F_2): 15N at an unknown distance (d2d_2) from the pivot.
    2. Explain the concept

    The Principle of Moments states that for a body in equilibrium, the sum of clockwise moments about a point is equal to the sum of anticlockwise moments about the same point.

    The formula for a moment is:

    Moment=Force×Perpendicular distance from the pivot\text{Moment} = \text{Force} \times \text{Perpendicular distance from the pivot}
    τ=F×d\tau = F \times d
    3. Show the solution

    To balance the ruler, we set the moment of the first force equal to the moment of the second force:

    F1×d1=F2×d2F_1 \times d_1 = F_2 \times d_2

    Given values:

    • F1=10NF_1 = 10\text{N}
    • d1=30cmd_1 = 30\text{cm}
    • F2=15NF_2 = 15\text{N}
    • d2=?d_2 = ?

    Calculation:

    10N×30cm=15N×d210\text{N} \times 30\text{cm} = 15\text{N} \times d_2
    300=15×d2300 = 15 \times d_2

    Now, solve for d2d_2:

    d2=30015d_2 = \frac{300}{15}
    d2=20cmd_2 = 20\text{cm}
    4. Identify the answer

    Comparing our result to the given options, 20cm corresponds to option C.

    5. Tip

    When solving "balancing" problems, always ensure your units are consistent. Since the distance is given in cm, your answer will also be in cm. Also, remember that the "pivot" acts as the fulcrum—always measure your distances from that specific point, not from the ends of the rule!

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  13. 13.

    Which of the following statements is Not true about atoms?

    1. A.Atom of different elements have different atomic weights
    2. B.The mass of an atom is concentrated in the nucleus
    3. C.An atom is made up of a nucleus and number of electrons
    4. D.Atoms of all elements are identical
    Show answer

    Answer: D. Atoms of all elements are identical

    AI explanation

    Analysis

    This question tests your fundamental understanding of Atomic Theory, specifically the properties of atoms as described by Dalton’s Atomic Theory and modern nuclear physics. We need to identify the statement that is scientifically incorrect.

    Concept Explanation
    • Atomic Structure: An atom consists of a central, dense nucleus (containing protons and neutrons) and surrounding electrons that orbit the nucleus. Because protons and neutrons are much heavier than electrons, almost all the mass of an atom is concentrated in the nucleus.
    • Elements: An element is defined by its atomic number (number of protons). Atoms of different elements have different numbers of protons and neutrons, which results in different atomic weights (mass numbers).
    • Dalton's Atomic Theory (Refined): While John Dalton originally proposed that all atoms of an element are identical, modern science has shown that isotopes exist. However, the statement "Atoms of all elements are identical" is fundamentally false because atoms of different elements (e.g., Hydrogen vs. Gold) have different structures, different numbers of subatomic particles, and different chemical properties.
    Step-by-Step Evaluation
    • Option A: True. Different elements have different numbers of protons and neutrons, leading to different atomic weights.
    • Option B: True. The nucleus contains the nucleons (protons and neutrons), which account for over 99.9% of the atom's mass.
    • Option C: True. This is the standard definition of an atom's structure.
    • Option D: False. Atoms of different elements are distinct and have different properties. Even within the same element, isotopes exist, but the statement that all elements are identical is scientifically incorrect.
    Conclusion

    The statement that is not true is that atoms of all elements are identical. They vary significantly in their subatomic composition and physical properties.

    Exam Tip: When you see a question asking for what is "NOT true," read all options carefully. Often, three options will be clearly correct facts, and the "odd one out" is your answer. Remember: Elements are defined by their differences, not their similarities!

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  14. 14.

    A satellite revolving around the earth is kept on its orbit by?

    1. A.Centripetal forces only
    2. B.Centripetal and frictional forces
    3. C.Centrifugal forces only
    4. D.Centripetal and centrifugal forces
    Show answer

    Answer: A. Centripetal forces only

    AI explanation

    Analysis

    The question asks for the physical force responsible for maintaining a satellite's orbital motion around the Earth. To answer this, we must distinguish between the forces acting on the satellite and the nature of circular motion.

    Concept Explanation
    1. Circular Motion: For any object to move in a circular path, there must be a net force directed toward the center of the circle. This is called centripetal force.
    2. The Role of Gravity: In the case of a satellite, the gravitational pull of the Earth acts as the centripetal force. Without this gravitational pull, the satellite would move in a straight line into space (Newton’s First Law of Motion).
    3. Centrifugal Force: This is a "pseudo" or fictitious force that appears to act on an object in a rotating frame of reference. It is not a real force acting on the satellite; rather, it is an effect of the satellite's inertia. Therefore, it is not what "keeps" the satellite in orbit.
    4. Frictional Forces: Space is a vacuum, so there is no air resistance or friction to consider in this context.
    Step-by-Step Solution
    • Step 1: Identify the requirement for circular motion. A satellite in orbit is essentially performing uniform circular motion.
    • Step 2: Identify the force providing the inward pull. The Earth's gravitational field provides a constant radial force directed toward the center of the Earth.
    • Step 3: Apply the definition of centripetal force. Since the gravitational force is directed toward the center of the orbit, it satisfies the definition of a centripetal force.
    • Step 4: Evaluate the options. Since only the centripetal force (provided by gravity) is responsible for the orbital motion, and centrifugal force is not a real force acting on the satellite, Option A is the only physically correct description.
    Conclusion

    The satellite is kept in its orbit solely by the gravitational force, which acts as the centripetal force.

    Exam Tip: Always remember that "Centrifugal force" is a common distractor in physics exams. In reality, it is just the inertia of the body trying to move in a straight line. When asked what keeps an object in a circular path, the answer is always centripetal force.

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  15. 15.

    Semiconductor is a class of solid whose conductivity increases with an increase in

    1. A.Pressure
    2. B.Temperature
    3. C.Current
    4. D.Voltage
    Show answer

    Answer: B. Temperature

    AI explanation

    Analysis

    The question asks for the physical factor that causes an increase in the electrical conductivity of a semiconductor material.

    Concept Explanation

    In physics, materials are classified based on their electrical conductivity. Semiconductors (like Silicon and Germanium) have properties that fall between conductors (like copper) and insulators (like glass).

    • Conductors: As temperature increases, the atoms in the metal lattice vibrate more, causing more collisions with electrons. This increases resistance and decreases conductivity.
    • Semiconductors: At absolute zero, a semiconductor acts like an insulator because its valence band is full and its conduction band is empty. However, as the temperature increases, thermal energy is provided to the electrons. This energy allows electrons to break free from their covalent bonds and jump from the valence band to the conduction band.
    • Result: The increase in the number of free charge carriers (electrons and holes) leads to a significant decrease in resistance, which means the conductivity increases.
    Step-by-Step Solution
    1. Identify the nature of semiconductors: Semiconductors rely on the excitation of electrons across a small energy gap (band gap).
    2. Analyze the effect of temperature: When heat is applied, the thermal energy provides enough kinetic energy for electrons to overcome the band gap.
    3. Relate to conductivity: Conductivity (σ\sigma) is directly proportional to the number of charge carriers. Since temperature increases the number of charge carriers in a semiconductor, it directly increases the conductivity.
    4. Evaluate other options: Pressure, current, and voltage do not fundamentally change the intrinsic charge carrier concentration of a semiconductor in the same way temperature does.
    Conclusion

    The conductivity of a semiconductor is highly sensitive to temperature. As temperature rises, more charge carriers become available, making the material more conductive.

    Exam Tip: Always remember the "Semiconductor Rule": Temperature Up, Resistance Down, Conductivity Up. This is the opposite of what happens in metallic conductors!

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  16. 16.

    A radioactive isotope has a decay constant of 10−6^{-6}s−1^{-1}. Calculate its half-life.

    1. A.5.93 x 106s
    2. B.6.93 x 105s
    3. C.6.93 x 109s
    4. D.5.93 x 107s
    Show answer

    Answer: B. 6.93 x 105s

    AI explanation

    Analysis

    To solve this problem, we need to find the relationship between the decay constant (λ\lambda) and the half-life (T1/2T_{1/2}) of a radioactive substance.

    Concept

    The half-life of a radioactive isotope is the time required for half of the radioactive nuclei in a sample to decay. The mathematical relationship between the half-life (T1/2T_{1/2}) and the decay constant (λ\lambda) is given by the formula:

    T1/2=ln⁡(2)λT_{1/2} = \frac{\ln(2)}{\lambda}

    Where:

    • ln⁡(2)\ln(2) is the natural logarithm of 2, which is approximately 0.693.
    • λ\lambda is the decay constant.
    Solution

    Step 1: Identify the given values.

    • Decay constant (λ\lambda) = 10−6 s−110^{-6} \text{ s}^{-1}

    Step 2: Apply the formula.

    T1/2=0.693λT_{1/2} = \frac{0.693}{\lambda}
    T1/2=0.69310−6T_{1/2} = \frac{0.693}{10^{-6}}

    Step 3: Simplify the expression. When you divide by a negative power of 10, it is the same as multiplying by the positive power of 10:

    T1/2=0.693×106T_{1/2} = 0.693 \times 10^6

    Step 4: Convert to standard form. To express 0.693×1060.693 \times 10^6 in standard scientific notation: Move the decimal point one place to the right:

    T1/2=6.93×105 sT_{1/2} = 6.93 \times 10^5 \text{ s}
    Conclusion

    Comparing our result to the given options, we can see that our calculated value matches option B.

    Exam Tip: Always remember that ln⁡(2)≈0.693\ln(2) \approx 0.693. If you ever forget the formula, just remember that the half-life and decay constant are inversely proportional; a very small decay constant means a very long half-life!

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  17. 17.

    When an athlete perspires after running, he loses heat through

    1. A.Evaporation
    2. B.Conduction
    3. C.Radiation
    4. D.Convection
    Show answer

    Answer: A. Evaporation

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  18. 18.

    Which of the following is obtained when a magenta is mixed with green colour?

    1. A.Yellow
    2. B.Blue
    3. C.White
    4. D.Red
    Show answer

    Answer: C. White

    AI explanation

    Analysis

    The question asks for the result of mixing the secondary color magenta with the primary color green. This falls under the study of Additive Color Mixing, which is a fundamental concept in Physics (specifically in the study of Light).

    Concept Explanation

    In the additive color system (the RGB model), colors are created by mixing light.

    • Primary Colors: Red, Green, and Blue.
    • Secondary Colors: These are formed by mixing two primary colors: • Magenta = Red + Blue • Cyan = Green + Blue • Yellow = Red + Green

    When you mix a secondary color with its complementary primary color, you get white light.

    • The complement of Green is Magenta.
    • The complement of Red is Cyan.
    • The complement of Blue is Yellow.
    Step-by-Step Solution
    1. Identify the components: We are mixing Magenta and Green.
    2. Break down Magenta: As established, Magenta is a combination of Red light and Blue light (Magenta=Red+BlueMagenta = Red + Blue).
    3. Combine with Green: Now, add the Green light to the mixture: Result=(Red+Blue)+GreenResult = (Red + Blue) + Green
    4. Observe the result: The combination of the three primary colors of light (Red + Green + Blue) produces White light.
    Conclusion

    When you mix magenta light with green light, the three primary colors of the spectrum are present, resulting in white light.

    Exam Tip: Remember the "Color Triangle." If you draw a triangle with Red, Green, and Blue at the corners, the colors in the middle (Magenta, Cyan, Yellow) are the secondary colors. Any line drawn through the center of this triangle connecting a primary color to its opposite secondary color will always result in white.

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  19. 19.

    I.Chemical II.Sound III.Electricity Which of the above forms of energy can directly be converted to light energy?

    1. A.I and II only
    2. B.II and III only
    3. C.I, II and III
    4. D.I and III only
    Show answer

    Answer: D. I and III only

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  20. 20.

    Myopic defects in the human eye can be corrected through the use of a

    1. A.Concave Mirror
    2. B.Concave lens
    3. C.Prism
    4. D.Convex lens
    Show answer

    Answer: B. Concave lens

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  21. 21.

    A train with an initial velocity of 20ms−1ms^{-1} is subjected to a uniform deceleration of 2ms−2ms^{-2}. The time required to bring the train to a complete halt is

    1. A.40s
    2. B.10s
    3. C.20s
    4. D.5s
    Show answer

    Answer: B. 10s

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  22. 22.

    A body which weighs 50N in air displaces 3.7kg of water when partially immersed in water. Calculate the upthrust on the body?

    1. A.8.7N
    2. B.37.0N
    3. C.87.0N
    4. D.13.0N
    Show answer

    Answer: B. 37.0N

    AI explanation

    1. Analyze the Question

    We are given:

    • Weight of the body in air (WairW_{air}) = 50 N
    • Mass of water displaced (mm) = 3.7 kg
    • We need to find the Upthrust acting on the body.
    2. Explain the Concept

    According to Archimedes' Principle, the upthrust on an object immersed in a fluid is equal to the weight of the fluid displaced by the object.

    The formula for weight is:

    Weight=mass×acceleration due to gravity (W=mg)Weight = mass \times acceleration\ due\ to\ gravity\ (W = mg)

    In physics problems for JAMB, unless otherwise specified, we use the standard value for acceleration due to gravity (gg) as 10 m/s².

    3. Show the Solution
    • Step 1: Identify the mass of the displaced water. m=3.7 kgm = 3.7\text{ kg}
    • Step 2: Calculate the weight of the displaced water using g=10 m/s²g = 10\text{ m/s²}. Upthrust=m×gUpthrust = m \times g Upthrust=3.7 kg×10 m/s²Upthrust = 3.7\text{ kg} \times 10\text{ m/s²} Upthrust=37.0 NUpthrust = 37.0\text{ N}

    The weight of the body in air (50 N) is extra information provided to test if you understand that upthrust depends only on the weight of the displaced fluid, not the weight of the object itself.

    4. Identify the Answer

    Comparing our result (37.0 N) with the given options: A. 8.7N B. 37.0N C. 87.0N D. 13.0N

    The correct option is B.

    5. Exam Tip

    Always remember: Upthrust = Weight of displaced fluid. If the question gives you the volume of the displaced fluid instead of the mass, remember to multiply the volume by the density of the fluid to get the mass first (m=ρVm = \rho V), then multiply by gg. Don't get distracted by the weight of the object in air unless the question asks for the "apparent weight" (which is Wair−UpthrustW_{air} - Upthrust).

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  23. 23.

    The frequency of beats produced when two tunning forks of frequencies 258Hz and 270Hz are sounded close to each other

    1. A.6Hz
    2. B.264Hz
    3. C.528Hz
    4. D.12Hz
    Show answer

    Answer: D. 12Hz

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  24. 24.

    Vapour is said to be saturated on top of an enclosed liquid if _________

    1. A.The rate of condensation is greater than that of vapourization
    2. B.The rate of condensation is equal to that of vapourization
    3. C.There is neither condensation nor vaporization of the liquid
    4. D.The rate of condensation is less that that of vaporization
    Show answer

    Answer: B. The rate of condensation is equal to that of vapourization

    AI explanation

    Analysis of the Question

    The question asks for the condition that defines a saturated vapour in an enclosed space above a liquid. This is a fundamental concept in the study of Heat Energy and Kinetic Theory of Matter.

    Explanation of the Concept

    In an enclosed container, molecules at the surface of a liquid constantly escape into the space above (a process called vaporization or evaporation). Simultaneously, some of the vapour molecules collide with the liquid surface and return to the liquid state (a process called condensation).

    • Unsaturated Vapour: Initially, the rate of vaporization is higher than the rate of condensation.
    • Saturated Vapour: As more molecules enter the vapour phase, the pressure increases. Eventually, the number of molecules escaping the liquid per second becomes exactly equal to the number of molecules returning to the liquid per second. At this point, the vapour is said to be saturated, and the space above the liquid can hold no more vapour at that specific temperature.
    Step-by-Step Solution
    1. Identify the state of equilibrium: When a vapour is saturated, it is in a state of dynamic equilibrium.
    2. Analyze the rates: Dynamic equilibrium means that while both processes (vaporization and condensation) are still occurring, they are happening at the same rate.
    3. Evaluate the options: • If the rate of condensation were greater (Option A), the vapour would be decreasing. • If there were no vaporization or condensation (Option C), the system would be static, not dynamic. • If the rate of condensation were less (Option D), the vapour would still be unsaturated. • Since the rates must be equal for saturation to exist, Option B is the correct description.
    Conclusion

    Exam Tip: Always remember that "saturated" in physics often implies a state of dynamic equilibrium. Whether it is a saturated solution in Chemistry or a saturated vapour in Physics, the key is that the forward and backward processes are occurring at the same rate!

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  25. 25.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.

  26. 26.

    Which of the following statements is correct about a machine?

    1. A.Efficiency of a machine is always greater than I
    2. B.Efficiency decreases with an increase in friction
    3. C.Velocity ratio depends on friction
    4. D.Mechanical advantage increases with an increase in friction
    Show answer

    Answer: B. Efficiency decreases with an increase in friction

    AI explanation

    1. Analyze the question

    The question asks us to identify the correct relationship between a machine's efficiency, friction, velocity ratio, and mechanical advantage. To answer this, we must understand the fundamental principles of simple machines.

    2. Explain the concept
    • Efficiency (η\eta): This is the ratio of the work output to the work input, usually expressed as a percentage. It is also defined as the ratio of Mechanical Advantage (MA) to Velocity Ratio (VR): $η=MAVR×100%\eta = \frac{\text{MA}}{\text{VR}} \times 100\%$
    • Friction: In any real-world machine, friction is always present. Friction causes some of the input energy to be dissipated as heat. As friction increases, the work output decreases for the same amount of work input, which directly lowers the efficiency.
    • Velocity Ratio (VR): This is determined by the geometry or design of the machine (e.g., the number of pulleys or the length of a lever). It is independent of friction.
    • Mechanical Advantage (MA): This is the ratio of the load to the effort. Friction reduces the effective output force, meaning that as friction increases, the MA actually decreases.
    3. Show the solution
    • Option A: Efficiency is always less than 1 (or 100%) because no machine is perfectly frictionless. Therefore, A is incorrect.
    • Option B: Since efficiency is defined by how much input energy is successfully converted to useful output, and friction wastes energy as heat, an increase in friction will always result in a lower efficiency. This statement is correct.
    • Option C: Velocity ratio is a mechanical property based on the machine's construction (distance moved by effort / distance moved by load). Friction does not change the geometry of the machine. Therefore, C is incorrect.
    • Option D: Mechanical advantage is the ratio of load to effort. Friction opposes motion, requiring more effort to move the same load. This decreases the MA, not increases it. Therefore, D is incorrect.
    4. Identify the answer

    The correct statement is that efficiency decreases as friction increases.

    5. Tip

    When dealing with machine questions, remember the "Ideal vs. Real" rule:

    • Ideal Machine: Efficiency = 100% (No friction).
    • Real Machine: Efficiency < 100% (Friction is present).
    • Golden Rule: Friction is the enemy of efficiency! Whenever friction goes up, efficiency must go down.

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  27. 27.

    A satellite moves in a circular orbit of radius 4R round the earth. The acceleration of the satellite in terms of g is

    1. A.g16\frac{g}{16}
    2. B.g4\frac{g}{4}
    3. C.4g\frac{4}{g}
    4. D.16g\frac{16}{g}
    Show answer

    Answer: A. g16\frac{g}{16}

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  28. 28.

    A pool of water appears to be 1.00m deep when viewed vertically from above. What is the actual depth of the pool? [Refractive index of water = 1.33]

    1. A.13.300m
    2. B.0.750m
    3. C.1.013m
    4. D.1.330m
    Show answer

    Answer: D. 1.330m

    AI explanation

    1. Analyze the question

    We are given the apparent depth of a pool of water (how deep it looks) and the refractive index of water. We need to calculate the actual depth (the real physical depth of the pool).

    2. Explain the concept

    When light travels from a denser medium (water) to a rarer medium (air), it bends away from the normal. This causes objects submerged in water to appear shallower than they actually are. This phenomenon is described by the formula for Refractive Index (nn):

    n=Actual DepthApparent Depthn = \frac{\text{Actual Depth}}{\text{Apparent Depth}}

    Where:

    • nn = Refractive index of the medium (water)
    • Actual Depth = The real depth of the pool
    • Apparent Depth = The depth as perceived by an observer
    3. Show the solution

    Given:

    • Apparent Depth = 1.00 m1.00\,\text{m}
    • Refractive Index (nn) = 1.331.33

    Formula:

    n=Actual DepthApparent Depthn = \frac{\text{Actual Depth}}{\text{Apparent Depth}}

    Rearranging to find Actual Depth:

    Actual Depth=n×Apparent Depth\text{Actual Depth} = n \times \text{Apparent Depth}

    Calculation:

    Actual Depth=1.33×1.00 m\text{Actual Depth} = 1.33 \times 1.00\,\text{m}
    Actual Depth=1.33 m\text{Actual Depth} = 1.33\,\text{m}
    4. Identify the answer

    Comparing our result to the options provided, the correct value is 1.330 m1.330\,\text{m}. This matches option D.

    5. Tip

    When dealing with refraction problems, always remember: "Real is greater than Apparent." If you are looking at an object in water, the actual depth will always be greater than the apparent depth. If your calculation gives you a number smaller than the apparent depth, you likely swapped the numerator and denominator in your formula!

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  29. 29.

    The instrument used to view stars is the

    1. A.Prism binoculars
    2. B.Telescope
    3. C.Film projector
    4. D.Microscope
    Show answer

    Answer: B. Telescope

    AI explanation

    1. Analyze the question

    The question asks for the specific optical instrument designed for observing distant objects, specifically celestial bodies like stars.

    2. Explain the concept

    Optical instruments are devices that use lenses or mirrors to manipulate light. To choose the right one, we must consider the purpose of each:

    • Microscope: Used to magnify very small, nearby objects (like cells or bacteria).
    • Film Projector: Used to project images from a film onto a screen for viewing.
    • Prism Binoculars: Used for viewing distant terrestrial objects (like birds or scenery), but they are not powerful enough for deep space observation.
    • Telescope: Specifically designed to collect light from distant objects (like stars and planets) and bring them into focus, making them appear larger and brighter.
    3. Show the solution
    • Step 1: Evaluate the nature of stars. Stars are extremely distant, meaning they appear as tiny points of light to the naked eye.
    • Step 2: Identify the requirement. To see stars clearly, an instrument needs a large aperture (to collect as much light as possible) and a high magnification power.
    • Step 3: Match the requirement to the options. A telescope is the only instrument listed that is engineered to gather light from vast distances in space.
    4. Identify the answer

    Comparing the options, the Telescope is the correct instrument for viewing stars.

    5. Tip

    Think of the prefixes: "Micro-" means small (for small things), while "Tele-" comes from the Greek word meaning "far off" (for things far away). This simple trick will help you distinguish between a microscope and a telescope every time!

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  30. 30.

    Which of the following statements is NOT correct?

    1. A.Brownian motion is an evidence of the particle nature of matter
    2. B.Atoms combine to form molecules
    3. C.The molecules of matter are not in constant motion
    4. D.matter is made up of molecules
    Show answer

    Answer: C. The molecules of matter are not in constant motion

    AI explanation

    Analysis of the Question

    The question asks you to identify the incorrect statement among the four options provided regarding the nature of matter and the kinetic theory of matter.

    Concept Explanation: The Kinetic Theory of Matter

    To solve this, we must look at the fundamental principles of the Kinetic Theory of Matter:

    1. Matter is particulate: All matter is made up of tiny, discrete particles called atoms or molecules.
    2. Constant motion: These particles are in a state of continuous, random motion (this is what causes phenomena like diffusion and Brownian motion).
    3. Intermolecular forces: There are forces of attraction between these particles.
    4. Temperature relationship: The kinetic energy of these particles increases as the temperature increases.
    Step-by-Step Evaluation
    • Option A: Brownian motion is the random, zig-zag movement of particles suspended in a fluid. It is a direct result of the continuous bombardment of these particles by the fast-moving molecules of the fluid. This is indeed evidence that matter is made of particles. (Correct statement)
    • Option B: Atoms are the building blocks of matter. When atoms bond together, they form molecules (e.g., two Hydrogen atoms and one Oxygen atom form a water molecule). (Correct statement)
    • Option C: The kinetic theory explicitly states that molecules of matter are always in constant motion, even in solids (where they vibrate about fixed positions). Therefore, stating they are not in constant motion contradicts the fundamental laws of physics. (Incorrect statement)
    • Option D: This is the basic definition of matter in physics and chemistry. (Correct statement)
    Conclusion

    Since the question asks for the statement that is NOT correct, Option C is the right choice because it contradicts the established kinetic theory of matter.

    Exam Tip

    When you see questions about the "Kinetic Theory of Matter," always remember the acronym "C.A.M.":

    • Constant motion.
    • Atoms/Molecules (matter is made of these).
    • Motion increases with temperature. If an option says particles are "stationary" or "not in motion," it is almost certainly the wrong statement!

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  31. 31.

    If the distance between the object and the pinhole of a pinhole camera is reduced by half the size of the image of the object

    1. A.Is quadrupled
    2. B.Is halved
    3. C.Remains the same
    4. D.Is double
    Show answer

    Answer: D. Is double

    AI explanation

    Analysis

    To solve this problem, we need to understand the relationship between the object distance, the image distance, and the size of the image in a pinhole camera.

    Concept

    A pinhole camera works on the principle of the rectilinear propagation of light. The relationship between the object height (hoh_o), image height (hih_i), object distance (uu), and image distance (vv) is given by the magnification formula:

    hiho=vu\frac{h_i}{h_o} = \frac{v}{u}

    Where:

    • hih_i = size of the image
    • hoh_o = size of the object
    • vv = distance from the pinhole to the image (fixed, as it is the length of the camera box)
    • uu = distance from the pinhole to the object

    From this formula, we can see that the size of the image (hih_i) is inversely proportional to the object distance (uu):

    hi∝1uh_i \propto \frac{1}{u}
    Step-by-Step Solution
    1. Initial state: Let the initial object distance be u1u_1 and the initial image size be hi1h_{i1}. $hi1=ho⋅vu1h_{i1} = \frac{h_o \cdot v}{u_1}$
    1. Change in distance: The distance is reduced by half, so the new object distance u2u_2 is: $u2=12u1u_2 = \frac{1}{2}u_1$
    1. New image size: Substitute u2u_2 into the formula to find the new image size hi2h_{i2}: $hi2=ho⋅vu2=ho⋅v12u1h_{i2} = \frac{h_o \cdot v}{u_2} = \frac{h_o \cdot v}{\frac{1}{2}u_1}$
    1. Simplify: $hi2=2⋅(ho⋅vu1)h_{i2} = 2 \cdot \left( \frac{h_o \cdot v}{u_1} \right)$ $hi2=2⋅hi1h_{i2} = 2 \cdot h_{i1}$

    The new image size is twice the original size.

    Conclusion

    When the distance between the object and the pinhole is halved, the image size becomes double the original size.

    Exam Tip

    Always remember the "Inverse Rule" for pinhole cameras: if you move the object closer, the image gets bigger; if you move it further away, the image gets smaller. Since the relationship is linear, if you divide the distance by 2, you multiply the size by 2.

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  32. 32.

    The rate of cooling of a heated quantity of liquid in an enclosure depends on the

    1. A.Pressure of the liquid
    2. B.Temperature in the enclosure
    3. C.Pressure of the enclosure
    4. D.Volume of the liquid
    Show answer

    Answer: B. Temperature in the enclosure

    AI explanation

    Analysis of the Question

    This question tests your understanding of Newton’s Law of Cooling. The law states that the rate at which an object (or liquid) loses heat to its surroundings is proportional to the difference in temperature between the object and its surroundings.

    Concept Explanation

    Newton’s Law of Cooling is expressed by the formula:

    dQdt=−k(T−Ts)\frac{dQ}{dt} = -k(T - T_s)

    Where:

    • dQdt\frac{dQ}{dt} is the rate of cooling (heat loss per unit time).
    • kk is a constant depending on the nature of the surface and the enclosure.
    • TT is the temperature of the liquid.
    • TsT_s is the temperature of the surroundings (the enclosure).

    From this formula, you can see that the rate of cooling depends directly on the temperature difference between the liquid and the enclosure. If the temperature of the enclosure (TsT_s) changes, the rate of cooling will change accordingly.

    Step-by-Step Solution
    1. Identify the variables: The rate of cooling is determined by the temperature gradient between the hot body and the environment.
    2. Evaluate the options: • A (Pressure of the liquid): Pressure does not directly dictate the rate of heat transfer in this context. • B (Temperature in the enclosure): As shown in the formula, the temperature of the surroundings (TsT_s) is a primary factor in determining how fast the liquid cools. • C (Pressure of the enclosure): While pressure can affect boiling points, it is not the primary factor for the rate of cooling in a standard enclosure. • D (Volume of the liquid): While volume affects the total heat capacity, the rate of cooling is primarily governed by the temperature difference and surface area, not the volume itself.
    Conclusion

    The rate of cooling is fundamentally dependent on the temperature difference between the liquid and its surroundings (the enclosure). Therefore, the temperature of the enclosure is the correct factor among the choices provided.

    Exam Tip

    When you see questions about "rate of cooling," always look for keywords related to temperature difference. Remember that the larger the difference between the hot object and the room (enclosure), the faster the object will cool down!

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  33. 33.

    A wire of length 10m is cooled from 50oC to 10oC. Calculate the decrease in the length of the wire. [c = 3 x 10-5K-1]

    1. A.1.8 x 10-4m
    2. B.1.5 x 10-4m
    3. C.1.2 x 10-2m
    4. D.1.8 x 10-3m
    Show answer

    Answer: C. 1.2 x 10-2m

    AI explanation

    Analysis

    To solve this problem, we need to calculate the change in length (ΔL\Delta L) of a material due to a change in temperature. This is a classic application of Linear Expansivity.

    Concept

    The formula for linear expansion is:

    ΔL=L0⋅α⋅Δθ\Delta L = L_0 \cdot \alpha \cdot \Delta \theta

    Where:

    • ΔL\Delta L = Change in length (what we are looking for)
    • L0L_0 = Original length of the wire (10 m10\text{ m})
    • α\alpha = Coefficient of linear expansivity (3×10−5 K−13 \times 10^{-5}\text{ K}^{-1})
    • Δθ\Delta \theta = Change in temperature (θ2−θ1\theta_2 - \theta_1)
    Solution

    Step 1: Identify the given values.

    • L0=10 mL_0 = 10\text{ m}
    • α=3×10−5 K−1\alpha = 3 \times 10^{-5}\text{ K}^{-1}
    • θ1=50∘C\theta_1 = 50^\circ\text{C}
    • θ2=10∘C\theta_2 = 10^\circ\text{C}

    Step 2: Calculate the change in temperature (Δθ\Delta \theta).

    Δθ=50∘C−10∘C=40∘C\Delta \theta = 50^\circ\text{C} - 10^\circ\text{C} = 40^\circ\text{C}

    (Note: A change in Celsius is equivalent to a change in Kelvin, so we can use 40 K40\text{ K}).

    Step 3: Substitute the values into the formula.

    ΔL=10×(3×10−5)×40\Delta L = 10 \times (3 \times 10^{-5}) \times 40

    Step 4: Perform the multiplication.

    ΔL=10×40×3×10−5\Delta L = 10 \times 40 \times 3 \times 10^{-5}
    ΔL=400×3×10−5\Delta L = 400 \times 3 \times 10^{-5}
    ΔL=1200×10−5\Delta L = 1200 \times 10^{-5}

    Step 5: Convert to standard form.

    ΔL=1.2×103×10−5\Delta L = 1.2 \times 10^3 \times 10^{-5}
    ΔL=1.2×10−2 m\Delta L = 1.2 \times 10^{-2}\text{ m}
    Conclusion

    Comparing our result with the given options, we find that 1.2×10−2 m1.2 \times 10^{-2}\text{ m} matches option C.

    Exam Tip: Always pay attention to the powers of ten. When multiplying numbers like 400×3400 \times 3, you get 12001200. Remember that 12001200 is the same as 1.2×1031.2 \times 10^3. When you multiply that by 10−510^{-5}, you simply add the exponents (3+(−5)=−23 + (-5) = -2). This quick mental math saves time in the exam hall!

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  34. 34.

    The heat required to raise a mass of a substance through 1K is known as

    1. A.Specific heat capacity
    2. B.Specific latent heat of vaporization
    3. C.Capacity latent heat of fusion
    4. D.Heat capacity
    Show answer

    Answer: D. Heat capacity

    AI explanation

    Analysis

    The question asks for the definition of the amount of heat energy required to increase the temperature of a specific mass of a substance by 1 Kelvin (or 1 degree Celsius).

    Concept Explanation

    To understand this, we must distinguish between Heat Capacity and Specific Heat Capacity:

    1. Heat Capacity (CC): This is defined as the quantity of heat required to raise the temperature of a given mass of a substance by 1K (or 1°C). Its unit is J/KJ/K. • Formula: C=mcC = mc (where mm is mass and cc is specific heat capacity).
    2. Specific Heat Capacity (cc): This is defined as the quantity of heat required to raise the temperature of unit mass (1kg) of a substance by 1K (or 1°C). Its unit is J/kg⋅KJ/kg \cdot K.

    Since the question specifies "a mass of a substance" (implying the total mass of the object in question) rather than "unit mass," it refers to the total heat capacity of that object.

    Step-by-Step Solution
    • Step 1: Identify the variables. We are looking for the heat (QQ) required for a temperature change (ΔT=1K\Delta T = 1K) for a mass (mm).
    • Step 2: Recall the relationship Q=CΔTQ = C \Delta T.
    • Step 3: If ΔT=1K\Delta T = 1K, then Q=CQ = C.
    • Step 4: Compare this to the options. Option A refers to "unit mass," while Option D refers to the mass of the substance as a whole. Therefore, the definition provided matches Heat Capacity.
    Conclusion

    This is consistent with the standard physics definition where "Heat Capacity" is the energy required to raise the temperature of the entire body by 1K, whereas "Specific Heat Capacity" is reserved for a unit mass (1kg).

    Exam Tip

    A simple way to remember the difference:

    • Specific = 1kg (Think of "Specific" as "Specific unit mass").
    • Heat Capacity = The whole object (Think of it as the "Capacity" of the whole object to hold heat).

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  35. 35.

    An object is placed 15cm in front of a plane mirror. If the mirror is moved further 5cm away from the object and the image is

    1. A.80cm
    2. B.40cm
    3. C.50cm
    4. D.70cm
    Show answer

    Answer: B. 40cm

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  36. 36.

    A boy in a barber's shop sits between two parallel mirrors. The number of images observed by him will be

    1. A.Infinite
    2. B.Ten
    3. C.Eight
    4. D.Forty
    Show answer

    Answer: A. Infinite

    AI explanation

    Analysis

    The question asks for the number of images formed when an object (the boy) is placed between two plane mirrors that are positioned parallel to each other.

    Concept Explanation

    When two plane mirrors are placed parallel to each other (at an angle of θ=0∘\theta = 0^\circ), light rays reflect back and forth between the two surfaces. Each reflection creates a new image of the previous image.

    The formula for the number of images (nn) formed by two plane mirrors inclined at an angle θ\theta is:

    n=360∘θ−1n = \frac{360^\circ}{\theta} - 1

    In this scenario, since the mirrors are parallel, the angle between them is 0∘0^\circ. Substituting this into the formula:

    n=360∘0∘−1n = \frac{360^\circ}{0^\circ} - 1

    Mathematically, division by zero is undefined, which in physical optics implies that the reflections continue indefinitely. As the light bounces between the two parallel surfaces, it creates an infinite series of images that get progressively fainter.

    Step-by-Step Solution
    1. Identify the setup: The mirrors are parallel, meaning the angle between them is 0∘0^\circ.
    2. Apply the principle: Because the mirrors are parallel, light rays are trapped in a cycle of infinite reflections.
    3. Conclusion: Each reflection produces an image, and because the reflections never cease, the number of images formed is infinite.
    Identify the Answer

    The correct option is A.

    Exam Tip

    Whenever you see a question about mirrors at an angle, remember:

    • Parallel mirrors (0∘0^\circ): Infinite images.
    • Perpendicular mirrors (90∘90^\circ): 36090−1=3\frac{360}{90} - 1 = 3 images.
    • General rule: If the result of 360θ\frac{360}{\theta} is an even number, the number of images is 360θ−1\frac{360}{\theta} - 1. If it is an odd number, the number of images is 360θ−1\frac{360}{\theta} - 1 (if the object is off-center) or 360θ\frac{360}{\theta} (if the object is exactly on the bisector).

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  37. 37.

    What happens to a water pool on a day when the humidity of the air is very low?

    1. A.Temperature decreases
    2. B.Slow evaporation
    3. C.Temperature increases
    4. D.Rapid evaporation
    Show answer

    Answer: D. Rapid evaporation

    AI explanation

    Analysis

    The question asks about the effect of low atmospheric humidity on a body of water (a pool). To answer this, we need to understand the relationship between the air's moisture content and the process of evaporation.

    Concept: Evaporation and Humidity
    • Evaporation is the process where liquid molecules gain enough kinetic energy to escape into the air as vapor.
    • Humidity refers to the amount of water vapor already present in the air.
    • Relative Humidity is a measure of how "full" the air is with water vapor. When humidity is low, the air is "dry" and has a high capacity to hold more water vapor.
    • The Relationship: Evaporation occurs most rapidly when the air is dry because there is a large concentration gradient between the water surface (saturated) and the surrounding air (unsaturated). The air "demands" more moisture, causing water molecules to leave the pool surface at a much faster rate.
    Step-by-Step Solution
    1. Identify the condition: The air has very low humidity, meaning it is very dry.
    2. Evaluate the process: Because the air is dry, the space immediately above the water pool is not saturated with water vapor.
    3. Determine the effect: Molecules from the pool will escape into the air more frequently to try and reach an equilibrium. This process is known as evaporation.
    4. Conclusion: Since the air is dry (low humidity), the rate at which these molecules escape is significantly higher than on a humid day. Therefore, evaporation happens rapidly.
    Why other options are incorrect:
    • A & C: While evaporation can cause a slight cooling effect (latent heat of vaporization), the primary physical phenomenon described by the state of the air is the rate of the phase change, not the temperature change of the pool.
    • B: Slow evaporation occurs when humidity is high (the air is already saturated and cannot easily accept more water vapor).
    Exam Tip

    Think of a dry sponge: if you place a dry sponge in a room with high humidity, it won't dry out quickly. If you place it in a room with low humidity (like a room with a dehumidifier), it dries out very fast. The air acts like a sponge for water vapor—the drier the air, the faster it "soaks up" the water from the pool.

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  38. 38.

    The relative density of a liquid is the ratio of the

    1. A.Mass of water to the mass of an equal volume of liquid
    2. B.Upthrust in the liquid to the upthrust in water
    3. C.Density of water to the density of the liquid
    4. D.Upthrust in water to the upthrust in the liquid
    Show answer

    Answer: B. Upthrust in the liquid to the upthrust in water

    AI explanation

    1. Analyze the question

    The question asks for the definition of "relative density" (also known as specific gravity) in the context of a liquid. You need to identify which ratio correctly represents this physical property.

    2. Explain the concept

    Relative density is a dimensionless quantity that compares the density of a substance to the density of a reference substance (usually water for liquids and solids).

    The formula is:

    Relative Density=Density of the liquidDensity of water\text{Relative Density} = \frac{\text{Density of the liquid}}{\text{Density of water}}

    According to Archimedes' Principle, the upthrust (buoyant force) experienced by an object fully immersed in a fluid is equal to the weight of the fluid displaced.

    • Upthrust in liquid (ULU_L) = V×ρL×gV \times \rho_L \times g
    • Upthrust in water (UWU_W) = V×ρW×gV \times \rho_W \times g

    If you take the ratio of the upthrust in the liquid to the upthrust in water:

    ULUW=V⋅ρL⋅gV⋅ρW⋅g=ρLρW\frac{U_L}{U_W} = \frac{V \cdot \rho_L \cdot g}{V \cdot \rho_W \cdot g} = \frac{\rho_L}{\rho_W}

    This ratio is exactly the definition of relative density.

    3. Show the solution
    • Option A: This is the inverse of the density ratio.
    • Option B: As shown in the derivation above, the ratio of the upthrust in the liquid to the upthrust in water is equal to the ratio of their densities, which is the definition of relative density.
    • Option C: This is the inverse of the definition of relative density.
    • Option D: This is the inverse of the ratio in Option B.

    Comparing our derivation to the options, Option B is the correct physical representation.

    4. Identify the answer

    The correct option is B.

    5. Tip

    When dealing with "Relative Density" questions, always remember the "Reference" is the denominator. Since we are finding the relative density of a liquid, water is the reference, so water must be the denominator in the density ratio. Because upthrust is directly proportional to density, the ratio of upthrusts follows the same pattern as the ratio of densities.

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  39. 39.

    A projectile is fired from the ground level with a velocity of 300ms−1ms^{-1} at an angle of a 30o to the horizontal. Calculate the time taken to reach the maximum height? [g = 10ms−2ms^{-2}]

    1. A.30s
    2. B.20s
    3. C.25s
    4. D.15s
    Show answer

    Answer: D. 15s

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  40. 40.

    A dynamo primarily converts

    1. A.Mechanical energy into electrical energy
    2. B.Electrical energy into kinetic energy
    3. C.Potential energy into kinetic energy
    4. D.Kinetic energy into potential energy
    Show answer

    Answer: A. Mechanical energy into electrical energy

    AI explanation

    Analysis

    The question asks for the primary energy conversion process that occurs within a dynamo. To answer this, we need to understand the function of a dynamo in the context of electromagnetic induction.

    Concept Explanation

    A dynamo is an electrical generator that creates direct current (DC) using a commutator. The fundamental principle behind its operation is Faraday’s Law of Electromagnetic Induction.

    1. Input: You provide mechanical energy (usually by rotating a coil of wire within a magnetic field or rotating a magnet inside a coil).
    2. Process: As the coil rotates, it cuts through the magnetic flux lines. This change in magnetic flux induces an electromotive force (EMF) or voltage across the ends of the coil.
    3. Output: This induced voltage causes a current to flow, resulting in electrical energy.
    Step-by-Step Solution
    • Step 1: Identify the input. A dynamo requires physical motion (rotation) to function. This motion is a form of mechanical energy.
    • Step 2: Identify the output. The purpose of a dynamo is to generate electricity to power devices or charge batteries. This is electrical energy.
    • Step 3: Compare with the options. • Option A: Mechanical energy →\rightarrow Electrical energy (Matches our analysis). • Option B: Electrical →\rightarrow Kinetic (This describes an electric motor, not a dynamo). • Option C & D: These describe changes in mechanical states, not the generation of electricity.
    Conclusion

    A dynamo is designed to take mechanical work (rotation) and convert it into electrical power. Therefore, it converts mechanical energy into electrical energy.

    Exam Tip: Remember the "Motor vs. Generator" rule:

    • Generator (Dynamo): Mechanical →\rightarrow Electrical (Think: "I generate electricity from movement").
    • Motor: Electrical →\rightarrow Mechanical (Think: "I move things using electricity").

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  41. 41.

    Which of the following instruments can be used to measure current in an a.c circuit?

    1. A.Hot wire ammeter
    2. B.Moving coil ammeter
    3. C.Tangent galvanometer
    4. D.Moving coil galvanometer
    Show answer

    Answer: A. Hot wire ammeter

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  42. 42.

    If the magnification of a virtual image formed by an object 10cm from a convex less is 3, then the focal length of the lens is

    1. A.10cm
    2. B.20cm
    3. C.25cm
    4. D.15cm
    Show answer

    Answer: D. 15cm

    AI explanation

    1. Analyze the question

    We are given:

    • Object distance (uu) = 10 cm10\text{ cm}
    • Magnification (mm) = 33
    • The image is virtual.
    • We need to find the focal length (ff) of the convex lens.
    2. Explain the concept

    For a lens, magnification (mm) is defined as the ratio of the image distance (vv) to the object distance (uu):

    m=vum = \frac{v}{u}

    Since the image is virtual, the image distance (vv) must be treated as negative in the lens formula. The lens formula is:

    1f=1u+1v\frac{1}{f} = \frac{1}{u} + \frac{1}{v}
    3. Show the solution

    Step 1: Find the image distance (vv). Using the magnification formula:

    m=vum = \frac{v}{u}
    3=v103 = \frac{v}{10}
    v=3×10=30 cmv = 3 \times 10 = 30\text{ cm}

    Because the image is virtual, we assign a negative sign to vv:

    v=−30 cmv = -30\text{ cm}

    Step 2: Calculate the focal length (ff) using the lens formula.

    1f=1u+1v\frac{1}{f} = \frac{1}{u} + \frac{1}{v}
    1f=110+1−30\frac{1}{f} = \frac{1}{10} + \frac{1}{-30}
    1f=110−130\frac{1}{f} = \frac{1}{10} - \frac{1}{30}

    Find the common denominator (which is 30):

    1f=3−130\frac{1}{f} = \frac{3 - 1}{30}
    1f=230\frac{1}{f} = \frac{2}{30}
    1f=115\frac{1}{f} = \frac{1}{15}

    Therefore:

    f=15 cmf = 15\text{ cm}
    4. Identify the answer

    The calculated focal length is 15 cm15\text{ cm}, which matches option D.

    5. Tip

    Always remember the Sign Convention: For thin lenses, real images have a positive image distance (vv), while virtual images have a negative image distance (vv). If you forget this sign, you will likely get the wrong focal length!

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  43. 43.

    What is the angular magnification of a telescope having objective and eyepiece lenses of a focal lengths 30cm and 3cm respectively?

    1. A.60
    2. B.10
    3. C.30
    4. D.90
    Show answer

    Answer: B. 10

    AI explanation

    Analysis

    The question asks for the angular magnification (MM) of an astronomical telescope. We are given the focal length of the objective lens (fof_o) and the focal length of the eyepiece lens (fef_e).

    Concept

    For an astronomical telescope in normal adjustment (where the final image is formed at infinity), the angular magnification is defined as the ratio of the focal length of the objective lens to the focal length of the eyepiece lens.

    The formula is:

    M=fofeM = \frac{f_o}{f_e}

    Where:

    • MM = Angular magnification
    • fof_o = Focal length of the objective lens
    • fef_e = Focal length of the eyepiece lens
    Solution

    Step 1: Identify the given values.

    • fo=30 cmf_o = 30\text{ cm}
    • fe=3 cmf_e = 3\text{ cm}

    Step 2: Apply the formula.

    M=30 cm3 cmM = \frac{30\text{ cm}}{3\text{ cm}}

    Step 3: Calculate the result.

    M=10M = 10

    The angular magnification is 10. This means the telescope makes the object appear 10 times larger than it would appear to the naked eye.

    Conclusion

    Comparing our result to the given options: A. 60 B. 10 C. 30 D. 90

    The correct option is B.

    Exam Tip

    When dealing with telescope problems, always remember that the objective lens is the one with the longer focal length (it gathers more light), while the eyepiece has the shorter focal length. If you ever get a value less than 1, you likely flipped the fraction—check your work to ensure the larger number is on top!

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  44. 44.

    Shadows and eclipse result from the

    1. A.Reflection of light
    2. B.Rectilinear propagation of light
    3. C.Diffraction of light
    4. D.Refraction of light
    Show answer

    Answer: B. Rectilinear propagation of light

    AI explanation

    Analysis

    The question asks for the fundamental principle of light that explains why shadows are formed and why eclipses (solar and lunar) occur.

    Concept Explanation

    The behavior of light is governed by several principles. To understand this question, we look at how light travels:

    • Rectilinear Propagation of Light: This principle states that light travels in a straight line in a uniform medium. Because light cannot bend around corners or obstacles, when an opaque object is placed in the path of a light source, the light is blocked. The region behind the object where light cannot reach is what we perceive as a shadow.
    • Eclipses: An eclipse is essentially a large-scale shadow. A solar eclipse occurs when the Moon passes between the Sun and the Earth, casting a shadow on the Earth. A lunar eclipse occurs when the Earth passes between the Sun and the Moon, casting a shadow on the Moon. Both phenomena rely entirely on the fact that light travels in straight lines and is blocked by these celestial bodies.
    Step-by-Step Solution
    1. Evaluate Option A (Reflection): Reflection involves light bouncing off a surface (like a mirror). While reflection creates images, it is not the cause of shadows.
    2. Evaluate Option B (Rectilinear propagation): Since light travels in straight lines, it cannot "bend" around an opaque object. Therefore, the space behind the object remains dark, forming a shadow. This perfectly explains both shadows and eclipses.
    3. Evaluate Option C (Diffraction): Diffraction is the bending of light around the edges of small obstacles or through small apertures. This is a wave property that usually causes light to spread out, not create sharp shadows.
    4. Evaluate Option D (Refraction): Refraction is the bending of light as it passes from one medium to another (e.g., from air to glass). This is responsible for lenses and prisms, not shadows.
    Conclusion

    The formation of shadows and eclipses is a direct consequence of the fact that light travels in straight lines. Therefore, the correct principle is the rectilinear propagation of light.

    Exam Tip: Whenever you see questions about "shadows," "pinhole cameras," or "eclipses," immediately associate them with the rectilinear propagation of light. These three are the classic JAMB examples for this concept!

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  45. 45.

    The impulse of a force is deduced from Newton's second law as

    1. A.F = ma
    2. B.F = m( v−ut\frac{v - u}{t}
    3. C.F = mg
    4. D.F = mv - mu
    Show answer

    Answer: D. F = mv - mu

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  46. 46.

    What force has to be exerted on a mass 60kg to give it an acceleration of 10ms−2ms^{-2} vertically upwards? [g = 10ms−2ms^{-2}

    1. A.300N
    2. B.600N
    3. C.1200N
    4. D.400N
    Show answer

    Answer: C. 1200N

    AI explanation

    Analysis

    To solve this problem, we need to understand the forces acting on an object being accelerated vertically. When an object is moved upwards, the applied force must not only overcome the weight of the object (gravity) but also provide the additional force required to produce the specified acceleration.

    Concept

    According to Newton's Second Law of Motion, the net force (FnetF_{net}) acting on an object is the product of its mass (mm) and its acceleration (aa):

    Fnet=maF_{net} = ma

    When an object is moving vertically upwards, the net force is the difference between the applied upward force (FF) and the downward force due to gravity (weight, W=mgW = mg).

    F−mg=maF - mg = ma

    Rearranging to find the applied force (FF):

    F=m(g+a)F = m(g + a)
    Solution

    Step 1: Identify the given values

    • Mass (mm) = 60 kg
    • Acceleration (aa) = 10 ms−2ms^{-2}
    • Acceleration due to gravity (gg) = 10 ms−2ms^{-2}

    Step 2: Apply the formula Substitute the values into the equation F=m(g+a)F = m(g + a):

    • F=60×(10+10)F = 60 \times (10 + 10)
    • F=60×20F = 60 \times 20
    • F=1200 NF = 1200 \, N
    Conclusion

    The force required to lift the 60kg mass with an upward acceleration of 10 ms−2ms^{-2} is 1200 N.

    Exam Tip: Always remember that when an object accelerates upwards, you add the acceleration to gravity (g+ag + a). If the object were accelerating downwards, you would subtract the acceleration from gravity (g−ag - a). This simple distinction is a common trap in JAMB Physics questions!

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  47. 47.

    Which of the following does Not use magnetic effect of current to function?

    1. A.Lead acid accumulator
    2. B.An electric bell
    3. C.A moving coil galvanometer
    4. D.A telephone receiver
    Show answer

    Answer: A. Lead acid accumulator

    AI explanation

    Analysis of the Question

    The question asks us to identify which of the listed devices does not rely on the magnetic effect of an electric current to operate. The magnetic effect of current (electromagnetism) occurs when an electric current flowing through a conductor creates a magnetic field around it.

    Explanation of Concepts
    • Magnetic Effect of Current: This principle is used in devices where an electric current is converted into mechanical motion or sound through the interaction of magnetic fields.
    • Electrochemical Effect: Some devices function by storing or converting chemical energy into electrical energy (or vice versa) through chemical reactions, rather than using magnetic fields.
    Step-by-Step Evaluation
    1. Lead acid accumulator (Option A): This is a type of rechargeable battery. It stores energy through chemical reactions (electrochemical process) between lead plates and sulfuric acid. It does not use magnetism to store or release energy.
    2. Electric bell (Option B): An electric bell uses an electromagnet. When current flows, the electromagnet attracts a hammer to strike the bell. This is a direct application of the magnetic effect of current.
    3. Moving coil galvanometer (Option C): This device measures small electric currents. It works by placing a current-carrying coil in a magnetic field, which experiences a torque (turning effect). This is a classic application of the magnetic effect of current.
    4. Telephone receiver (Option D): A telephone receiver uses an electromagnet to convert varying electrical signals into mechanical vibrations of a diaphragm, which produces sound. This also relies on the magnetic effect of current.
    Conclusion

    Comparing these, the lead acid accumulator is the only device that functions based on chemical principles rather than the magnetic effect of an electric current.

    Exam Tip: Whenever you see questions about "effects of current," remember the three main categories:

    • Heating effect: Electric iron, kettle, filament bulb.
    • Magnetic effect: Electric bell, motor, galvanometer, transformer.
    • Chemical effect: Electrolysis, electroplating, lead-acid batteries (accumulators).

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  48. 48.

    Calculate the temperature of 6 moles of an ideal gas at a pressure of 7.6 x 106Nm−2Nm^{-2} with a volume of 10-3m3. [R = 8.3jmol-1K-1]

    1. A.201oC
    2. B.126oC
    3. C.153oC
    4. D.185oC
    Show answer

    Answer: C. 153oC

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