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JAMB 2022

2022 JAMB Physics Past Questions and Answers

The 2022 JAMB Physics past questions with answers: 40 objective questions from the 2022 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.

    The eclipse of the moon occurs when?

    1. A.the moon reflects the rays from the sun to the earth
    2. B.the moon comes exactly between the earth and the sun
    3. C.the earth comes exactly between the moon and the sun
    4. D.the sun comes exactly between the earth and the moon
    Show answer

    Answer: C. the earth comes exactly between the moon and the sun

    AI explanation

    Analysis of the Question

    This question tests your understanding of rectilinear propagation of light and the relative positions of celestial bodies (the Sun, the Earth, and the Moon) during an eclipse.

    Concept Explanation

    An eclipse occurs when one celestial body moves into the shadow of another.

    • Solar Eclipse: Occurs when the Moon passes between the Sun and the Earth, casting a shadow on the Earth.
    • Lunar Eclipse (Eclipse of the Moon): Occurs when the Earth passes directly between the Sun and the Moon. Because the Earth is opaque, it blocks the sunlight that would normally reach the Moon, casting a shadow on the Moon's surface.
    Step-by-Step Solution
    1. Identify the components: We have the Sun (the light source), the Earth, and the Moon.
    2. Analyze the condition for a Lunar Eclipse: For the Moon to be "eclipsed" (darkened), the light from the Sun must be obstructed by an object.
    3. Determine the positioning: If the Earth moves into the path of the light rays traveling from the Sun toward the Moon, the Earth will cast a shadow on the Moon.
    4. Evaluate the options: • Option A describes the normal state of the Moon (reflecting sunlight), not an eclipse. • Option B describes a Solar Eclipse. • Option C describes the Earth blocking the Sun's light from reaching the Moon, which is the definition of a Lunar Eclipse. • Option D is physically impossible in this context, as the Sun is the source of light.
    Conclusion

    The Earth must be positioned exactly between the Sun and the Moon to block the light and create a lunar eclipse. This matches option C.

    Exam Tip

    To remember the difference, look at the name of the eclipse:

    • Lunar Eclipse: The Moon is the one being hidden (Lunar = Moon). The Earth is in the middle.
    • Solar Eclipse: The Sun is the one being hidden (Solar = Sun). The Moon is in the middle.

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  2. 2.

    A cell whose internal resistance is 0.55Ω\Omega delivers a current of 4 A to an external resistor. The lost voltage of the cell is?

    1. A.4.00 V
    2. B.2.20 V
    3. C.0.15 V
    4. D.8.00 V
    Show answer

    Answer: B. 2.20 V

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  3. 3.

    Which component of fiber-optic connector has a provision of entry for the fibre along with the fixation to connector housing?

    1. A.coupling device
    2. B.cable
    3. C.ferrule
    4. D.connector housing
    Show answer

    Answer: B. cable

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  4. 4.

    A person standing waist-deep in a swimming pool appears to have short legs because of light?

    1. A.diffraction
    2. B.refraction
    3. C.reflection
    4. D.interference
    Show answer

    Answer: B. refraction

    AI explanation

    Analysis

    The question asks for the physical phenomenon responsible for the visual distortion of an object (in this case, a person's legs) when viewed through a medium different from air (water).

    Concept Explanation

    This phenomenon is explained by Refraction. Refraction is the bending of light as it travels from one medium to another of different optical density (e.g., from water to air).

    1. Optical Density: Water is optically denser than air.
    2. Bending of Light: When light rays reflected from the person's legs travel from the water into the air, they move from a denser medium to a less dense medium. According to Snell's Law, the light rays bend away from the normal.
    3. Apparent Position: Our eyes trace these light rays back in a straight line. Because the rays have bent, the brain perceives the legs to be at a shallower depth than they actually are. This makes the legs appear shorter or "raised" compared to the rest of the body above the water.
    Step-by-Step Solution
    • Step 1: Identify the media involved: Water (denser) and Air (less dense).
    • Step 2: Recognize that light travels at different speeds in these two media.
    • Step 3: Apply the principle of refraction: As light leaves the water, it changes direction (bends).
    • Step 4: Conclude that the change in the path of light causes the image to appear displaced, leading to the illusion of shortened legs.
    • Diffraction (Option A) involves the spreading of waves around obstacles.
    • Reflection (Option C) involves light bouncing off a surface.
    • Interference (Option D) involves the superposition of two or more waves.

    None of these explain the change in the apparent position of an object submerged in a liquid.

    Correct Answer

    The correct option is B.

    Exam Tip

    Whenever you see a question about objects appearing "bent," "shortened," or "raised" in water (like a stick in a pool or a coin at the bottom of a cup), the answer is almost always Refraction. Think of it as the "bending" of light!

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  5. 5.

    One of the following is a scalar quantity?

    1. A.weight
    2. B.momentum
    3. C.potential energy
    4. D.displacement
    Show answer

    Answer: C. potential energy

    AI explanation

    Analysis

    The question asks us to identify which of the given physical quantities is a scalar quantity.

    Concept Explanation

    In physics, quantities are categorized into two main types based on their properties:

    1. Scalar Quantities: These are physical quantities that have magnitude only. They do not have a specific direction. Examples include mass, time, temperature, distance, speed, and energy.
    2. Vector Quantities: These are physical quantities that have both magnitude and direction. Examples include force, velocity, acceleration, displacement, momentum, and weight.
    Step-by-Step Evaluation

    Let’s examine each option:

    • A. Weight: Weight is the force of gravity acting on an object (W=mgW = mg). Since force is a vector quantity (it always acts downwards towards the center of the Earth), weight is a vector.
    • B. Momentum: Momentum is the product of mass and velocity (p=mvp = mv). Since velocity is a vector, momentum is also a vector.
    • C. Potential Energy: Energy is the capacity to do work. It is defined by its magnitude (the amount of energy) and does not have a direction associated with it. Therefore, potential energy is a scalar.
    • D. Displacement: Displacement is the shortest distance between two points in a specified direction. Because it requires a direction, it is a vector.
    Conclusion

    Comparing our analysis to the options, only potential energy fits the definition of a scalar quantity.

    Exam Tip: A simple trick to remember the difference is the "Direction Test." Ask yourself, "Does it make sense to say '5 meters to the North'?" If yes, it's a vector (like displacement). If you ask, "Does it make sense to say '5 Joules to the North'?" it sounds nonsensical, which confirms it is a scalar!

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  6. 6.

    The mercury column in the barometer at notational  atmospheric pressure has a height of?

    1. A.0.76 cm at see level
    2. B.760 cm at sea level
    3. C.7.6 cm at sea level
    4. D.76 cm at sea level
    Show answer

    Answer: D. 76 cm at sea level

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  7. 7.

    In order to view the sun, the most suitable instrument to use is?

    1. A.helioscope
    2. B.telescope
    3. C.stroboscope
    4. D.sun meter
    Show answer

    Answer: A. helioscope

    AI explanation

    Analysis

    The question asks for the most suitable instrument specifically designed for observing the sun. We need to distinguish between general optical instruments and those designed with safety features for solar observation.

    Concept Explanation

    When observing the sun, the primary concern is safety. The sun emits intense light and harmful radiation (including ultraviolet and infrared rays) that can cause permanent eye damage or blindness if viewed directly through standard optical instruments.

    • Telescope: A general-purpose instrument used to magnify distant objects. A standard telescope is dangerous for solar viewing because it concentrates the sun's rays, which can burn the retina instantly.
    • Stroboscope: An instrument used to make a cyclically moving object appear to be slow-moving or stationary. It is not used for viewing celestial bodies.
    • Helioscope: A specialized type of telescope or an attachment to a telescope specifically designed for viewing the sun. It includes filters or projection methods to reduce the intensity of the sun's light to a safe level for the human eye.
    Step-by-Step Solution
    1. Evaluate the options: We eliminate the stroboscope immediately as it is for motion analysis.
    2. Compare Telescope and Helioscope: While a telescope is used for astronomy, it requires significant modification (solar filters) to be safe for the sun. A helioscope is the specific term for an instrument designed for this purpose.
    3. Conclusion: The helioscope is the dedicated device for solar observation, making it the most suitable and correct answer in the context of physics instruments.
    Exam Tip

    When you see questions about "viewing the sun," always look for terms with the prefix "helio-", which is the Greek word for "sun" (e.g., helioscope, heliocentric). This is a great way to identify the correct answer even if you haven't memorized every instrument!

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  8. 8.

    Which of the following liquid is a poor conductor of electricity?

    1. A.Distilled water
    2. B.Tap water
    3. C.Sea water
    4. D.Drinking water
    Show answer

    Answer: A. Distilled water

    AI explanation

    Analysis

    The question asks us to identify which of the listed liquids is a poor conductor of electricity. To solve this, we must understand what makes a liquid conduct electricity.

    Concept Explanation

    For a liquid to conduct electricity, it must contain free ions (charged particles) that can move through the solution to carry an electric current. This process is known as electrolytic conduction.

    • Pure water (distilled water) consists of H2OH_2O molecules. It is a covalent compound and does not dissociate into ions to any significant extent. Therefore, it is an insulator.
    • Tap water, sea water, and drinking water contain dissolved mineral salts (like sodium chloride, magnesium, and calcium salts). These salts dissociate into ions (Na+Na^+, Cl−Cl^-, etc.) when dissolved in water, making these liquids good conductors of electricity.
    Step-by-Step Solution
    1. Evaluate Sea water: Contains a high concentration of dissolved salts (sodium chloride). It is an excellent conductor.
    2. Evaluate Tap water: Contains dissolved minerals and chlorine from water treatment plants. It is a moderate conductor.
    3. Evaluate Drinking water: Similar to tap water, it contains dissolved minerals necessary for health, which allow it to conduct electricity.
    4. Evaluate Distilled water: This is water that has been purified through distillation, removing all dissolved salts and minerals. Because it lacks free ions, it cannot conduct electricity effectively.
    Conclusion

    Since distilled water lacks the dissolved ions necessary to facilitate the flow of electric current, it is classified as a poor conductor (or an insulator) compared to the other options provided.

    Exam Tip: Always remember that "pure" water is a poor conductor. If you see a question about water conductivity, look for terms like "distilled," "deionized," or "pure." If the water has "impurities" (minerals/salts), it will conduct electricity!

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  9. 9.

    The relationship between the coefficient of linear expansion α\alpha and volumetric expansion (γ\gamma) is-----------------

    1. A.γ\gamma = α−3\alpha ^{-3}
    2. B.γ\gamma = α\alpha
    3. C.3α\alpha
    4. D.γ\gamma = α3\alpha ^{3}
    Show answer

    Answer: C. 3α\alpha

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  10. 10.

    An object 40 cm high is 30cm from the pin hole camera. If the height of the image formed is 20 cm. What is the distance of the image from the pin height?

    1. A.15 cm
    2. B.70 cm
    3. C.40 cm
    4. D.40 cm
    Show answer

    Answer: A. 15 cm

    AI explanation

    1. Analyze the Question

    We are given the height of an object (hoh_o), the distance of the object from the pinhole (uu), and the height of the image formed (hih_i). We need to find the distance of the image from the pinhole (vv).

    2. Explain the Concept

    A pinhole camera works on the principle of the rectilinear propagation of light. The relationship between the object height, image height, and their respective distances from the pinhole is defined by the principle of similar triangles. The formula is:

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

    Where:

    • hih_i = height of the image
    • hoh_o = height of the object
    • vv = distance of the image from the pinhole
    • uu = distance of the object from the pinhole
    3. Show the Solution

    Given data:

    • Height of object (hoh_o) = 40 cm
    • Distance of object (uu) = 30 cm
    • Height of image (hih_i) = 20 cm
    • Distance of image (vv) = ?

    Step-by-step calculation: Substitute the values into the formula:

    2040=v30\frac{20}{40} = \frac{v}{30}

    Simplify the fraction on the left:

    12=v30\frac{1}{2} = \frac{v}{30}

    Now, cross-multiply to solve for vv:

    2v=302v = 30
    v=302v = \frac{30}{2}
    v=15 cmv = 15 \text{ cm}
    4. Identify the Answer

    The calculated distance of the image from the pinhole is 15 cm. This matches option A.

    5. Tip

    In pinhole camera problems, always remember that the ratio of the image height to the object height is equal to the ratio of their distances from the pinhole (magnification). If the image is smaller than the object, the image distance must be smaller than the object distance!

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  11. 11.

    A semiconductor is formed by?

    1. A.co-ordinate bonds
    2. B.electrovalent bonds
    3. C.a substance free of bonds
    4. D.covalent bonds
    Show answer

    Answer: D. covalent bonds

    AI explanation

    1. Analyze the question

    The question asks for the type of chemical bonding responsible for the structure of a semiconductor. Semiconductors are materials that have electrical conductivity between that of a conductor and an insulator.

    2. Explain the concept

    Semiconductors, such as Silicon (Si) and Germanium (Ge), belong to Group IV of the periodic table. Each atom in a semiconductor crystal has four valence electrons. To achieve a stable octet configuration, each atom shares its four valence electrons with four neighboring atoms. This sharing of electrons creates a strong, stable lattice structure known as a covalent bond.

    In these materials, the electrons are held firmly in these bonds at absolute zero temperature, making the material an insulator. However, as temperature increases or through a process called "doping," these covalent bonds can be broken, releasing electrons that allow the material to conduct electricity.

    3. Show the solution
    • Electrovalent (Ionic) bonds involve the transfer of electrons, which is characteristic of salts like NaCl, not semiconductors.
    • Co-ordinate (Dative) bonds involve one atom donating a lone pair of electrons to another, which is not the primary structure of elemental semiconductors.
    • Covalent bonds involve the sharing of electron pairs between atoms. In a silicon crystal, every silicon atom is covalently bonded to four other silicon atoms, forming the tetrahedral structure that defines the semiconductor.

    Therefore, the crystalline structure of a semiconductor is held together by covalent bonds.

    4. Identify the answer

    The correct option is D.

    5. Exam Tip

    When you see questions about semiconductors in JAMB, always remember the "Group IV" rule. Elements in Group IV (Silicon, Germanium) are the most common semiconductors, and they always form covalent bonds to create their crystal lattice. If you are asked about "doping," remember that it involves adding impurities to these covalent structures to increase conductivity!

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  12. 12.

    Tyres are treaded to?

    1. A.increase weight of tyres
    2. B.increase friction
    3. C.increase its longevity
    4. D.look good
    Show answer

    Answer: B. increase friction

    AI explanation

    Analysis

    The question asks for the physical purpose of the patterns (treads) carved into the surface of vehicle tyres.

    Concept Explanation

    In physics, friction is the force that opposes the relative motion between two surfaces in contact. For a vehicle to move, stop, or turn safely, there must be sufficient friction between the tyre and the road surface.

    • Smooth surfaces: When a tyre is smooth (bald), there is very little grip, especially on wet roads. Water can form a thin film between the tyre and the road, causing the vehicle to "hydroplane" or skid.
    • Treaded surfaces: Treads are the grooves cut into the tyre. They serve two main purposes: • Channeling water: They act as drainage channels to push water away from the contact patch, allowing the rubber to maintain direct contact with the road. • Increasing grip: The edges of the tread patterns dig into the road surface (especially on loose surfaces like gravel or mud), which significantly increases the coefficient of friction between the tyre and the road.
    Step-by-Step Solution
    1. Evaluate Option A: Increasing the weight of the tyre is not a goal; in fact, manufacturers try to keep tyres as light as possible to improve fuel efficiency.
    2. Evaluate Option B: Treads create a rougher surface profile. By increasing the surface area contact and providing a path for debris/water to escape, the tyre gains a better "grip" on the road. This grip is the physical manifestation of increased friction.
    3. Evaluate Option C: While treads wear down over time, the primary purpose of the design is safety (friction), not necessarily to make the tyre last longer.
    4. Evaluate Option D: Aesthetics are a secondary consideration for manufacturers, but it is not the scientific reason for the existence of treads.
    Conclusion

    Treads are essential for safety because they ensure the vehicle can maintain traction. By increasing the grip on the road, they increase the frictional force available for braking and steering.

    Exam Tip

    Whenever you see a question about "treads," "spikes on shoes," or "grooves on soles," always associate them with increasing friction. Conversely, if a question asks how to reduce friction, look for answers involving "lubrication," "ball bearings," or "streamlining."

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  13. 13.

    Which expression gives magnetic flux?

    1. A.qVB sinθ\theta
    2. B.μϕI2πr\frac{\mu \phi I}{2 \pi r}
    3. C.BA cos θ\theta
    4. D.-N dϕdt\frac{d \phi}{dt}
    Show answer

    Answer: C. BA cos θ\theta

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  14. 14.

    A car starts from rest and covers a distance of 40 m in 10 s. Calculate the magnitude of its acceleration

    1. A.3.20 ms−2^{-2}
    2. B.0.25 ms−2^{-2}
    3. C.0.80 ms−2^{-2}
    4. D.4.00 ms−2^{-2}
    Show answer

    Answer: C. 0.80 ms−2^{-2}

    AI explanation

    1. Analyze the Question

    We are given the following information about a car's motion:

    • Initial velocity (uu) = 0 ms−10 \text{ ms}^{-1} (since it starts from rest)
    • Distance covered (ss) = 40 m40 \text{ m}
    • Time taken (tt) = 10 s10 \text{ s}
    • We need to find the acceleration (aa).
    2. Explain the Concept

    To solve this, we use the equations of uniformly accelerated motion. Specifically, the second equation of motion relates distance, initial velocity, time, and acceleration:

    s=ut+12at2s = ut + \frac{1}{2}at^2

    Where:

    • ss is the distance
    • uu is the initial velocity
    • tt is the time
    • aa is the acceleration
    3. Show the Solution

    Step 1: Substitute the known values into the formula.

    40=(0×10)+12×a×(10)240 = (0 \times 10) + \frac{1}{2} \times a \times (10)^2

    Step 2: Simplify the equation. Since 0×10=00 \times 10 = 0:

    40=0+12×a×10040 = 0 + \frac{1}{2} \times a \times 100
    40=50a40 = 50a

    Step 3: Solve for aa.

    a=4050a = \frac{40}{50}
    a=0.8 ms−2a = 0.8 \text{ ms}^{-2}
    4. Identify the Answer

    Comparing our result to the given options: A. 3.20 ms−2^{-2} B. 0.25 ms−2^{-2} C. 0.80 ms−2^{-2} D. 4.00 ms−2^{-2}

    The calculated value matches Option C.

    5. Exam Tip

    Whenever you see the phrase "starts from rest," immediately note that u=0u = 0. This simplifies your equations significantly because the utut term disappears, leaving you with just s=12at2s = \frac{1}{2}at^2. This is a common shortcut in JAMB Physics to save you time!

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  15. 15.

    A reservoir is filled with liquid of density 2000 kgm−1^{-1}. Calculate the depth at which the pressure in the liquid will be equal to 9100 Nm−2^{-2} (g = 10 ms−2^{-2})

    1. A.0.262 m
    2. B.0.664 m
    3. C.0.819 m
    4. D.0.455 m
    Show answer

    Answer: D. 0.455 m

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  16. 16.

    A bar magnet is divided into two pieces, which of the following statement is correct?

    1. A.two new magnets are created
    2. B.the magnetic field of each separate piece becomes stronger
    3. C.the electric field is created
    4. D.the bar magnet is demagnetized
    Show answer

    Answer: A. two new magnets are created

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  17. 17.

    Which of these is a derived unit?

    1. A.Kilogram
    2. B.Metre
    3. C.Newton
    4. D.Second
    Show answer

    Answer: C. Newton

    AI explanation

    1. Analyze the question

    The question asks you to identify a "derived unit" from the given list. To answer this, we must distinguish between base units (fundamental units) and derived units in the International System of Units (SI).

    2. Explain the concept
    • Base Units: These are the fundamental units of measurement that do not depend on any other physical quantities. There are seven base units in the SI system, including: • Length (Metre, m) • Mass (Kilogram, kg) • Time (Second, s) • Electric Current (Ampere, A) • Temperature (Kelvin, K) • Amount of substance (Mole, mol) • Luminous intensity (Candela, cd)
    • Derived Units: These are units created by combining base units through multiplication or division to express other physical quantities (like speed, force, or pressure). For example, Force is measured in Newtons, which is derived from mass and acceleration (F=maF = ma), giving it the base unit equivalent of kg⋅m/s2kg \cdot m/s^2.
    3. Show the solution

    Let's evaluate each option:

    • A. Kilogram: This is the SI base unit for mass.
    • B. Metre: This is the SI base unit for length.
    • C. Newton: This is the unit of force. Since Force = Mass × Acceleration (kg×m/s2kg \times m/s^2), the Newton is a derived unit because it is composed of base units.
    • D. Second: This is the SI base unit for time.
    4. Identify the answer

    Since the Newton is the only unit on the list formed by combining base units, it is the correct answer.

    5. Tip

    A quick way to remember this for your JAMB exam is the "Big Seven" rule: If you can memorize the seven base units (Mass, Length, Time, Current, Temperature, Amount, Intensity), any other unit you encounter in Physics (like Joule, Watt, Pascal, or Newton) is almost certainly a derived unit!

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  18. 18.

    The secondary pigments consist of?

    1. A.blue, green, and violet
    2. B.yellow, green, and magenta
    3. C.magenta, yellow, and cyan
    4. D.red, green, and blue
    Show answer

    Answer: D. red, green, and blue

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  19. 19.

    In the formation of sea breeze, wind blows from?

    1. A.sky to land
    2. B.sea to sky
    3. C.land to sea
    4. D.sea to land
    Show answer

    Answer: D. sea to land

    AI explanation

    Analysis

    This question tests your understanding of convection currents and the specific heat capacity of land versus water. It is a classic topic in Physics under the study of Heat Transfer.

    Concept Explanation

    To understand sea breezes, you must remember two key principles:

    1. Specific Heat Capacity: Land has a lower specific heat capacity than water. This means land heats up and cools down much faster than the sea.
    2. Convection: Warm air is less dense and rises, creating a low-pressure area. Cooler, denser air moves in to replace the rising warm air.

    During the day:

    • The sun heats both the land and the sea.
    • Because land has a lower specific heat capacity, it gets hot much faster than the sea.
    • The air above the land becomes hot, expands, and rises (creating a low-pressure zone over the land).
    • The air over the sea remains relatively cooler and denser.
    • Nature seeks to balance this pressure difference, so the cooler air from the sea rushes in toward the land to replace the rising warm air. This movement of air is what we call a sea breeze.
    Step-by-Step Solution
    1. Identify the heat source: Solar radiation heats the land surface more rapidly than the water surface during the day.
    2. Determine air movement: The air over the land warms up and rises, creating a partial vacuum (low pressure) over the land.
    3. Establish the flow: High-pressure air over the cooler sea moves toward the low-pressure area over the warmer land.
    4. Conclusion: The wind direction is from the sea toward the land.
    Exam Tip

    Think of the name: A "Sea Breeze" is a breeze that comes from the sea. Conversely, a "Land Breeze" occurs at night when the land cools down faster than the sea, causing the wind to blow from the land to the sea.

    The correct option is D.

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  20. 20.

    The graph of pressure (P) against the reciprocal of the volume (I/V) in Boyles's law is a?

    1. A.hyperbola
    2. B.parabola
    3. C.curve
    4. D.straight line
    Show answer

    Answer: D. straight line

    AI explanation

    1. Analyze the Question

    The question asks for the shape of the graph obtained when plotting Pressure (PP) against the reciprocal of volume (1/V1/V) based on Boyle’s Law.

    2. Explain the Concept

    Boyle’s Law states that for a fixed mass of an ideal gas at a constant temperature, the pressure (PP) is inversely proportional to the volume (VV):

    P∝1VP \propto \frac{1}{V}

    To express this as an equation, we introduce a constant (kk):

    P=k×(1V)P = k \times \left(\frac{1}{V}\right)

    This equation follows the mathematical form of a linear equation, y=mx+cy = mx + c, where:

    • yy is the pressure (PP)
    • xx is the reciprocal of volume (1/V1/V)
    • mm (the gradient) is the constant (kk)
    • cc (the intercept) is 00
    3. Show the Solution
    • If you plot PP against VV, you get a hyperbola (because PP decreases as VV increases).
    • However, if you plot PP against 1/V1/V, you are essentially plotting yy against xx in a direct proportion relationship.
    • Since P=k(1/V)P = k(1/V), as 1/V1/V increases, PP increases at a constant rate.
    • A graph of a direct proportion (y=mxy = mx) always results in a straight line passing through the origin.
    4. Identify the Answer

    The graph of PP against 1/V1/V is a straight line. Therefore, the correct option is D.

    5. Exam Tip
    • Memory Trick: Remember the "Boyle's Law Graph Rule": • PP vs VV = Hyperbola (Curve) • PP vs 1/V1/V = Straight line • PVPV vs PP = Straight horizontal line (because PVPV is constant)
    • Always check the axes labels carefully in the exam hall; a small change in the variable (like 1/V1/V vs VV) completely changes the shape of the graph!

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  21. 21.

    An isotope has an initial activity of 120 Bq. 6 days later its activity is 15 Bq. The half-life is?

    1. A.3 days
    2. B.2 days
    3. C.1 day
    4. D.4 days
    Show answer

    Answer: B. 2 days

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  22. 22.

    If an object just begins to slide on a surface inclined at 30º to the horizontal,the coefficient of friction is?

    1. A.√3
    2. B.√32\frac{√3}{2}
    3. C.1√2\frac{1}{√2}
    4. D.1√3\frac{1}{√3}
    Show answer

    Answer: D. 1√3\frac{1}{√3}

    AI explanation

    1. Analyze the question

    The question asks for the coefficient of friction (μ\mu) when an object is placed on an inclined plane and is just about to slide. This is a classic mechanics problem involving equilibrium on an inclined plane.

    2. Explain the concept

    When an object is placed on an inclined plane at an angle θ\theta, two main forces act on it relative to the surface:

    • The component of weight acting down the plane: mgsin⁡θmg \sin\theta
    • The normal reaction (RR): mgcos⁡θmg \cos\theta
    • The frictional force (FF): μR\mu R

    When the object is "just about to slide," it is in a state of limiting equilibrium. At this point, the force pulling the object down the slope is exactly balanced by the maximum static frictional force:

    mgsin⁡θ=Fmg \sin\theta = F

    Since F=μRF = \mu R and R=mgcos⁡θR = mg \cos\theta, we have:

    mgsin⁡θ=μ(mgcos⁡θ)mg \sin\theta = \mu (mg \cos\theta)

    By dividing both sides by mgcos⁡θmg \cos\theta, we get the relationship:

    μ=sin⁡θcos⁡θ=tan⁡θ\mu = \frac{\sin\theta}{\cos\theta} = \tan\theta
    3. Show the solution

    Given:

    • Angle of inclination (θ\theta) = 30∘30^\circ
    • Formula: μ=tan⁡θ\mu = \tan\theta

    Substitute the value of θ\theta:

    μ=tan⁡(30∘)\mu = \tan(30^\circ)

    From trigonometric ratios:

    tan⁡(30∘)=13\tan(30^\circ) = \frac{1}{\sqrt{3}}

    Therefore, the coefficient of friction is 13\frac{1}{\sqrt{3}}.

    4. Identify the answer

    Comparing our result to the options provided: A. 3\sqrt{3} B. 32\frac{\sqrt{3}}{2} C. 12\frac{1}{\sqrt{2}} D. 13\frac{1}{\sqrt{3}}

    The correct option is D.

    5. Tip

    Always remember the "Angle of Repose" rule: The coefficient of static friction is equal to the tangent of the angle of inclination at which an object just begins to slide. If you forget the formula, just draw a quick free-body diagram and resolve the forces—it will always lead you back to tan⁡θ\tan\theta!

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  23. 23.

    A tuning fork having a frequency of 312 Hz emits a wave which has a wavelength of 1.10 m. Calculate the velocity of sound

    1. A.312.0 ms−1^{-1}
    2. B.110.0 ms−1^{-1}
    3. C.343.2 ms−1^{-1}
    4. D.686.4 ms−1^{-1}
    Show answer

    Answer: C. 343.2 ms−1^{-1}

    AI explanation

    1. Analyze the question

    We are given the frequency (ff) of a tuning fork and the wavelength (λ\lambda) of the sound wave it produces. We are asked to calculate the velocity (vv) of the sound wave.

    • Frequency (ff) = 312 Hz
    • Wavelength (λ\lambda) = 1.10 m
    2. Explain the concept

    In wave motion, the relationship between velocity, frequency, and wavelength is defined by the Wave Equation:

    v=f×λv = f \times \lambda

    Where:

    • vv is the velocity of the wave (measured in meters per second, ms−1^{-1})
    • ff is the frequency (measured in Hertz, Hz)
    • λ\lambda (lambda) is the wavelength (measured in meters, m)

    This formula tells us that the speed of a wave is simply the product of how many waves pass a point per second and the length of each individual wave.

    3. Show the solution

    Using the wave equation:

    v=f×λv = f \times \lambda

    Substitute the given values into the formula:

    v=312×1.10v = 312 \times 1.10

    Perform the multiplication:

    v=312×1.1v = 312 \times 1.1
    v=343.2 ms−1v = 343.2 \text{ ms}^{-1}
    4. Identify the answer

    Comparing our result to the given options: A. 312.0 ms−1^{-1} B. 110.0 ms−1^{-1} C. 343.2 ms−1^{-1} D. 686.4 ms−1^{-1}

    The calculated value matches option C.

    5. Tip

    When solving wave problems in JAMB, always check your units first. If the frequency is in Hz and the wavelength is in meters, your velocity will automatically be in ms−1^{-1}. If the wavelength were given in centimeters, you would need to convert it to meters (divide by 100) before multiplying!

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  24. 24.

    The gravitational pull on the moon is 16\frac{1}{6} that of the earth. If a body weighs 6.0 N on the moon, what will be the weight on the earth?

    1. A.6.0 N
    2. B.5.0 N
    3. C.12.0 N
    4. D.36.0 N
    Show answer

    Answer: D. 36.0 N

    AI explanation

    Analysis

    The question asks us to find the weight of an object on Earth, given its weight on the Moon and the relationship between the gravitational pull of the two bodies.

    Concept

    Weight (WW) is the force of gravity acting on an object's mass (mm). It is calculated using the formula:

    W=mgW = mg

    where gg is the acceleration due to gravity.

    Since the mass (mm) of an object remains constant regardless of location, the ratio of weights on two different planets is directly proportional to the ratio of their gravitational accelerations:

    WmoonWearth=gmoongearth\frac{W_{moon}}{W_{earth}} = \frac{g_{moon}}{g_{earth}}
    Step-by-Step Solution
    1. Identify the given information: • Weight on the Moon (WmoonW_{moon}) = 6.0 N • Gravitational pull on the Moon is 16\frac{1}{6} that of the Earth, meaning: $gmoon=16×gearthg_{moon} = \frac{1}{6} \times g_{earth}$
    1. Set up the relationship: From the concept above, we know: $Wmoon=16×WearthW_{moon} = \frac{1}{6} \times W_{earth}$
    1. Substitute the values: $6.0 N=16×Wearth6.0\text{ N} = \frac{1}{6} \times W_{earth}$
    1. Solve for WearthW_{earth}: Multiply both sides by 6: $Wearth=6.0 N×6W_{earth} = 6.0\text{ N} \times 6$ $Wearth=36.0 NW_{earth} = 36.0\text{ N}$
    Conclusion

    The weight of the body on Earth is 36.0 N.

    Exam Tip

    Always remember that mass is constant (it doesn't change whether you are on the Moon, Earth, or in space), but weight changes depending on the local gravity. If you are moving from a place with lower gravity (the Moon) to a place with higher gravity (the Earth), your weight must increase!

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  25. 25.

    Water is not a good thermometric liquid because it?

    1. A.expands unevenly between 0 ºC and 4 ºC
    2. B.maintains fixed density
    3. C.has low freezing point
    4. D.wets glass
    Show answer

    Answer: A. expands unevenly between 0 ºC and 4 ºC

    Get a step-by-step AI explanation in the app

  26. 26.

    When the plate area of a capacitor increases?

    1. A.the voltage can withstand increase
    2. B.the capacitance decreases
    3. C.the capacitance is unaffected
    4. D.the capacitance increases
    Show answer

    Answer: D. the capacitance increases

    AI explanation

    Analysis

    The question asks about the relationship between the physical dimensions of a parallel-plate capacitor (specifically the plate area) and its capacitance.

    Concept Explanation

    The capacitance (CC) of a parallel-plate capacitor is determined by the formula:

    C=ε0εrAdC = \frac{\varepsilon_0 \varepsilon_r A}{d}

    Where:

    • CC is the capacitance (measured in Farads).
    • ε0\varepsilon_0 is the permittivity of free space (a constant).
    • εr\varepsilon_r is the relative permittivity (dielectric constant) of the material between the plates.
    • AA is the area of the overlapping plates.
    • dd is the distance between the plates.

    From this formula, we can see that the capacitance (CC) is directly proportional to the area (AA) of the plates. This means that if you increase the area of the plates, you are providing more space for charge to be stored at a given voltage, thereby increasing the capacitance.

    Step-by-Step Solution
    1. Identify the variables: We are looking at the effect of changing the area (AA) on the capacitance (CC).
    2. Apply the relationship: Since C∝AC \propto A, an increase in AA must result in an increase in CC.
    3. Evaluate the options: • A is incorrect because voltage rating is determined by the dielectric strength, not just the area. • B is incorrect because it suggests an inverse relationship. • C is incorrect because capacitance is physically dependent on the area. • D is correct because it aligns with the mathematical relationship C∝AC \propto A.
    Conclusion

    When the plate area of a capacitor increases, the capacitance increases because there is more surface area available to store electric charge.

    Exam Tip: Remember the mnemonic "C-A-D": Capacitance is proportional to Area and inversely proportional to Distance. If you remember this, you will never miss a question about how physical changes affect a capacitor!

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  27. 27.

    The vapour pressure?

    1. A.increases non-linearly with measuring temperature
    2. B.increases linearly with increasing temperature
    3. C.decreases linearly with increasing temperature
    4. D.decreases non-linearly ith measuring temperature
    Show answer

    Answer: A. increases non-linearly with measuring temperature

    AI explanation

    Analysis

    The question asks for the relationship between the vapour pressure of a liquid and its temperature. To answer this, we need to understand the kinetic theory of matter and how temperature affects the evaporation process.

    Concept Explanation

    Vapour pressure is the pressure exerted by a vapour in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system.

    1. Kinetic Energy: As temperature increases, the average kinetic energy of the molecules in the liquid increases.
    2. Evaporation: More molecules gain enough energy to overcome the intermolecular forces holding them in the liquid phase and escape into the gas phase.
    3. Pressure: As more molecules enter the vapour phase, the number of collisions with the walls of the container increases, thereby increasing the vapour pressure.
    4. The Curve: This relationship is not a straight line (linear). It follows an exponential growth pattern described by the Clausius-Clapeyron equation. Because the rate of increase accelerates as the temperature rises, the graph of vapour pressure versus temperature is a curve that bends upwards.
    Step-by-Step Solution
    • Step 1: Evaluate the relationship. We know that as temperature increases, vapour pressure increases. This immediately eliminates options C and D.
    • Step 2: Determine the nature of the increase. Because the relationship follows an exponential curve (as defined by the Clausius-Clapeyron relation), the increase is non-linear.
    • Step 3: Compare with options. Option A states it "increases non-linearly," which perfectly matches the physical behavior of vapour pressure. Option B is incorrect because the relationship is not a straight line.
    Conclusion

    The vapour pressure of a liquid increases non-linearly as the temperature increases. This is a fundamental concept in thermodynamics often tested in JAMB Physics.

    Exam Tip: Whenever you see a relationship involving "pressure" and "temperature" in a closed system (like vapour pressure or gas laws), always check if the relationship is linear or exponential. Most thermodynamic processes involving phase changes are non-linear!

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  28. 28.

    Which of the following is not a consequence of hydrogen bubbles covering the copper plate of a primary cell?

    1. A.formation of hydrogen bubbles on the electrode
    2. B.increase in the resistance of the cell
    3. C.local action
    4. D.polarization
    Show answer

    Answer: C. local action

    AI explanation

    Analysis

    The question asks us to identify which of the listed phenomena is not a direct consequence of hydrogen bubbles accumulating on the copper plate (the positive electrode) of a primary cell, such as a Simple Voltaic Cell.

    Concept Explanation

    In a simple primary cell, chemical reactions produce hydrogen gas at the copper plate. When these bubbles collect on the plate, they create a layer that prevents the electrolyte from making proper contact with the electrode. This process is known as polarization.

    1. Polarization (Option D): This is the direct name for the accumulation of hydrogen bubbles on the positive electrode.
    2. Increase in internal resistance (Option B): Because the hydrogen gas is an insulator, it increases the internal resistance of the cell, which reduces the current flowing through the circuit.
    3. Formation of hydrogen bubbles (Option A): This is the physical event that causes the polarization.
    4. Local Action (Option C): This is a completely different defect. Local action occurs due to impurities in the zinc plate (the negative electrode), which cause small local circuits to form, leading to the consumption of the zinc even when the cell is not in use.
    Step-by-Step Solution
    • Step 1: Identify the effect of hydrogen bubbles. Hydrogen bubbles on the copper plate cause polarization.
    • Step 2: Recognize the impact of polarization. Polarization leads to an increase in internal resistance and a drop in the cell's electromotive force (e.m.f.).
    • Step 3: Evaluate "Local Action." Local action is specifically caused by impurities in the zinc electrode, not by the accumulation of hydrogen bubbles on the copper plate.
    • Step 4: Conclusion. Since local action is a separate defect caused by a different mechanism (impurities in the zinc), it is not a consequence of hydrogen bubbles on the copper plate.
    Answer

    The correct option is C.

    Exam Tip

    To remember the difference:

    • Polarization happens at the Copper plate (Positive) and is caused by Hydrogen gas.
    • Local Action happens at the Zinc plate (Negative) and is caused by Impurities in the zinc.
    • Think: Polarization = Positive plate; Local Action = Level of impurities.

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  29. 29.

    The main factor which affects the speed of sound wave is the?

    1. A.properties of the medium
    2. B.amplitude of the sound wave
    3. C.intensity of the sound wave
    4. D.loudness of the sound wave
    Show answer

    Answer: A. properties of the medium

    AI explanation

    Analysis

    The question asks us to identify the primary factor that determines how fast a sound wave travels through space. We need to look at the physical characteristics of sound propagation.

    Concept Explanation

    Sound is a mechanical wave, meaning it requires a material medium (like air, water, or steel) to travel. The speed of sound (vv) is determined by the physical properties of that medium, specifically its elasticity (or bulk modulus) and its density.

    The formula for the speed of sound in a medium is generally given by:

    v=Eρv = \sqrt{\frac{E}{\rho}}

    Where:

    • EE is the elastic property of the medium (how easily it returns to its shape after being compressed).
    • ρ\rho (rho) is the density of the medium.

    Because sound waves rely on the vibration of particles to transfer energy, the "stiffness" and "density" of the particles dictate how quickly that energy is passed along. Factors like amplitude, intensity, and loudness are characteristics of the sound wave itself, but they do not change the speed at which the wave moves through a specific medium.

    Step-by-Step Solution
    1. Evaluate Option B (Amplitude): Amplitude relates to the energy or volume of the sound, not the speed.
    2. Evaluate Option C (Intensity): Intensity is the power per unit area; it describes how "strong" the sound is, not its speed.
    3. Evaluate Option D (Loudness): Loudness is a subjective human perception of intensity. It does not affect the physical speed of the wave.
    4. Evaluate Option A (Properties of the medium): As shown in the formula v=E/ρv = \sqrt{E/\rho}, the speed is entirely dependent on the medium's elasticity and density. For example, sound travels faster in steel (high elasticity) than in air (low elasticity).
    Conclusion

    The speed of sound is independent of the wave's characteristics (like loudness or amplitude) and is strictly a function of the medium through which it travels. Therefore, the properties of the medium are the main factor.

    Exam Tip

    Remember the acronym "MED": Medium Effects Determine speed. If you are ever asked what affects the speed of a wave, always look for the medium's properties (temperature, density, elasticity) rather than the wave's features (frequency, amplitude, wavelength).

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  30. 30.

    According to kinetic molecular model in gases,

    1. A.the particles are closely packed together; they occupy minimum space are usually arranged in a regular pattern
    2. B.the particles vibrate about fixed positions and are held together by the strong intermolecular bonds between them
    3. C.the molecules are very far apart and occupy all the spaces made available to them
    4. D.the particles occur in clusters with molecules slightly further apart
    Show answer

    Answer: C. the molecules are very far apart and occupy all the spaces made available to them

    AI explanation

    Analysis of the Question

    This question tests your understanding of the Kinetic Molecular Theory (KMT), specifically how it describes the behavior and arrangement of gas particles compared to solids and liquids.

    Explanation of the Concept

    The Kinetic Molecular Theory provides a model to explain the behavior of matter in its three states:

    • Solids: Particles are packed closely together in a fixed, regular pattern. They only vibrate about fixed positions. (This describes Option A and B).
    • Liquids: Particles are close together but can move past one another. They have no fixed shape but have a fixed volume.
    • Gases: According to the KMT, gas molecules are in constant, random motion. Because the intermolecular forces between them are negligible, they are very far apart compared to their size. Consequently, they expand to fill the entire volume of any container they are placed in.
    Step-by-Step Solution
    1. Evaluate Option A: This describes the structure of a solid. Particles in a gas are not closely packed.
    2. Evaluate Option B: This also describes a solid. Gas particles do not have strong intermolecular bonds holding them in fixed positions.
    3. Evaluate Option C: This aligns perfectly with the KMT for gases. Because gas molecules have high kinetic energy and weak intermolecular forces, they spread out to occupy all available space.
    4. Evaluate Option D: This describes a state closer to a liquid or a dense fluid, not the ideal behavior of gas molecules as defined by the kinetic model.
    Conclusion

    The kinetic molecular model emphasizes that gas molecules are far apart and move randomly, allowing them to fill any container available to them.

    Exam Tip: When dealing with KMT questions, remember the "Space" rule: Solids = No space (packed), Liquids = Little space (sliding), Gases = Maximum space (far apart).

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  31. 31.

    The potential energy in an elastic string of force constant k, which has an extension X is?

    1. A.kX
    2. B.KX2^{2}
    3. C.½KX2^{2}
    4. D.½K
    Show answer

    Answer: C. ½KX2^{2}

    AI explanation

    Analysis

    The question asks for the formula for the potential energy (often called elastic potential energy or strain energy) stored in a stretched elastic string (or spring) with a force constant kk and an extension xx.

    Concept

    According to Hooke’s Law, the force FF required to stretch a spring is directly proportional to the extension xx, provided the elastic limit is not exceeded. This is expressed as:

    F=kxF = kx

    When you stretch a spring, you do work against the restoring force. This work is stored in the spring as Elastic Potential Energy (EpE_p).

    To find the energy, we look at the force-extension graph. The graph is a straight line passing through the origin. The work done (energy stored) is equal to the area under the force-extension graph.

    Solution
    1. Identify the shape: The graph of Force (FF) against Extension (xx) is a right-angled triangle.
    2. Calculate the area: The area of a triangle is given by: $Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$
    3. Substitute the variables: • Base = extension (xx) • Height = force (F=kxF = kx)
    4. Derive the formula: $Ep=12×x×(kx)E_p = \frac{1}{2} \times x \times (kx)$ $Ep=12kx2E_p = \frac{1}{2}kx^2$
    Conclusion

    The potential energy stored in the elastic string is 12kx2\frac{1}{2}kx^2. Comparing this to your options, it matches option C.

    Exam Tip

    Always remember that for any linear relationship (like Hooke's Law), the energy is always "half" of the product of the two variables (FF and xx). If you ever forget the formula, just sketch a quick triangle graph of FF against xx and calculate the area!

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  32. 32.

    Which of these is a second-class lever?

    1. A.sugar tongs
    2. B.claw hammer
    3. C.plier
    4. D.wheelbarrow
    Show answer

    Answer: D. wheelbarrow

    AI explanation

    1. Analyze the question

    The question asks us to identify a second-class lever from the given options. To solve this, we must understand the classification of levers based on the relative positions of the Fulcrum (F), Load (L), and Effort (E).

    2. Explain the concept

    Levers are classified into three types based on which component is in the middle:

    • First-class lever: The Fulcrum is between the Effort and the Load (F is in the middle). Examples: See-saw, scissors, pliers, claw hammer (when pulling a nail).
    • Second-class lever: The Load is between the Fulcrum and the Effort (L is in the middle). This type of lever always provides a mechanical advantage greater than 1, making it easier to lift heavy weights. Examples: Wheelbarrow, nutcracker, bottle opener.
    • Third-class lever: The Effort is between the Fulcrum and the Load (E is in the middle). Examples: Sugar tongs, tweezers, fishing rod.
    3. Show the solution

    Let's evaluate each option:

    • A. Sugar tongs: The effort is applied in the middle, between the fulcrum (the hinge) and the load (the sugar cube). This is a third-class lever.
    • B. Claw hammer: When used to pull a nail, the fulcrum is the head of the hammer, the load is the nail, and the effort is applied at the handle. The fulcrum is in the middle. This is a first-class lever.
    • C. Plier: The fulcrum is the hinge, the effort is applied at the handles, and the load is at the jaws. The fulcrum is in the middle. This is a first-class lever.
    • D. Wheelbarrow: The fulcrum is the wheel axle, the load is the material in the bucket, and the effort is applied at the handles. The load is in the middle, between the fulcrum and the effort. This is a second-class lever.
    4. Identify the answer

    Based on the classification, the wheelbarrow is the only second-class lever listed.

    5. Tip

    To remember the order of levers, use the mnemonic "FLE":

    • F (1st class): Fulcrum in the middle.
    • L (2nd class): Load in the middle.
    • E (3rd class): Effort in the middle.

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  33. 33.

    The amount of energy required to change a kilogram of ice block into water without a change in temperature is?

    1. A.specific latent heat of fusion of ice
    2. B.specific heat capacity of ice
    3. C.heat capacity of ice
    4. D.specific heat of vaporization of ice
    Show answer

    Answer: A. specific latent heat of fusion of ice

    AI explanation

    1. Analyze the question

    The question asks for the specific term used to describe the energy required to change the state of 1 kilogram of a substance (specifically ice to water) at a constant temperature.

    2. Explain the concept

    In physics, latent heat is the energy absorbed or released by a substance during a change in its physical state (phase change) that occurs without changing its temperature.

    • Specific Latent Heat of Fusion (LfL_f): This is the amount of heat energy required to change 1 kg of a substance from solid to liquid at its melting point without a change in temperature.
    • Specific Heat Capacity: This is the energy required to raise the temperature of 1 kg of a substance by 1 Kelvin (or 1°C). This involves a temperature change, which contradicts the question.
    • Specific Latent Heat of Vaporization: This is the energy required to change 1 kg of a substance from liquid to gas at its boiling point.
    3. Show the solution
    • The process described is the phase change from solid (ice) to liquid (water).
    • The condition "without a change in temperature" confirms that we are dealing with latent heat, not specific heat capacity.
    • Since the change is from solid to liquid (melting/fusion), the correct term is the specific latent heat of fusion.

    The formula is:

    Q=mLfQ = mL_f

    Where:

    • QQ = Heat energy
    • mm = Mass (1 kg)
    • LfL_f = Specific latent heat of fusion
    4. Identify the answer

    Comparing our explanation to the options provided, the correct term is the specific latent heat of fusion of ice. This matches option A.

    5. Exam Tip

    Memory Trick: Think of "Fusion" as "Fusing together" or "Melting." If you are melting ice into water, you are dealing with the Latent Heat of Fusion. If you are boiling water into steam (vapor), you are dealing with the Latent Heat of Vaporization. Always remember: Latent = Constant Temperature.

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  34. 34.

    A current of 0.5 A flows through a resistor when connected to a 40 V battery. How much energy is dispatched in 2 minutes?

    1. A.2400 J
    2. B.9600 J
    3. C.1500 J
    4. D.1200 J
    Show answer

    Answer: A. 2400 J

    AI explanation

    1. Analyze the Question

    We are given:

    • Current (II) = 0.5 A
    • Voltage (VV) = 40 V
    • Time (tt) = 2 minutes
    • We need to find the energy (EE) dispatched (or dissipated) by the resistor.
    2. Explain the Concept

    In electricity, the energy (EE) dissipated by a component is given by the formula:

    E=V×I×tE = V \times I \times t
    • VV is the potential difference in Volts (V).
    • II is the current in Amperes (A).
    • tt is the time in seconds (s).

    Important Note: In physics calculations, time must always be converted to seconds to match the SI unit of energy (Joules).

    3. Show the Solution

    Step 1: Convert time to seconds. Since 1 minute = 60 seconds:

    t=2×60=120 secondst = 2 \times 60 = 120 \text{ seconds}

    Step 2: Apply the formula.

    E=V×I×tE = V \times I \times t
    E=40 V×0.5 A×120 sE = 40 \text{ V} \times 0.5 \text{ A} \times 120 \text{ s}

    Step 3: Calculate.

    E=(40×0.5)×120E = (40 \times 0.5) \times 120
    E=20×120E = 20 \times 120
    E=2400 JE = 2400 \text{ J}
    4. Identify the Answer

    Comparing our result to the given options: A. 2400 J B. 9600 J C. 1500 J D. 1200 J

    The calculated value matches option A.

    5. Exam Tip

    Always watch out for units in JAMB Physics! If the time is given in minutes or hours, convert it to seconds immediately before plugging it into your formula. Also, remember that V×IV \times I gives you Power (PP) in Watts; so, you can also think of the formula as E=P×tE = P \times t.

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  35. 35.

    Consider the wave equation y = 5mm sin [1cm−1^{-1}x - 60s−1^{-1}t]. The wave number is?

    1. A.0.1 cm−1^{-1}
    2. B.10cm−1^{-1}
    3. C.1.0cm−1^{-1}
    4. D.2cm−1^{-1}
    Show answer

    Answer: C. 1.0cm−1^{-1}

    AI explanation

    1. Analyze the question

    You are given a standard wave equation: y=5mmsin⁡[1cm−1x−60s−1t]y = 5\text{mm} \sin[1\text{cm}^{-1}x - 60\text{s}^{-1}t]. You need to identify the wave number (kk) from this equation.

    2. Explain the concept

    The general equation for a progressive wave traveling in the positive x-direction is given by:

    y=Asin⁡(kx−ωt)y = A \sin(kx - \omega t)

    Where:

    • AA is the amplitude.
    • kk is the wave number (or angular wave number), which is the coefficient of xx.
    • ω\omega is the angular frequency, which is the coefficient of tt.
    • xx is the position.
    • tt is the time.

    By comparing the given equation to the general form, you can directly extract the value of kk.

    3. Show the solution

    Given the equation:

    y=5mmsin⁡[1cm−1x−60s−1t]y = 5\text{mm} \sin[1\text{cm}^{-1}x - 60\text{s}^{-1}t]

    Comparing this to the standard form y=Asin⁡(kx−ωt)y = A \sin(kx - \omega t):

    • The term multiplying xx is kk.
    • In your equation, the term multiplying xx is 1cm−11\text{cm}^{-1}.

    Therefore:

    k=1cm−1k = 1\text{cm}^{-1}
    4. Identify the answer

    Comparing our result to the provided options: A. 0.1cm−10.1\text{cm}^{-1} B. 10cm−110\text{cm}^{-1} C. 1.0cm−11.0\text{cm}^{-1} D. 2cm−12\text{cm}^{-1}

    The correct option is C.

    5. Tip

    When you see a wave equation, don't let the units (like mm, cm, or s) confuse you. Just look for the variable xx and the variable tt. The number attached to xx is always your wave number (kk), and the number attached to tt is always your angular frequency (ω\omega). Keep your eyes on the coefficients!

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  36. 36.

    A train of mass 1600 kg attains a speed of 25 ms−1^{-1} in 20 seconds. The power developed in the engine is?

    1. A.2.5 KW
    2. B.80 KW
    3. C.25 KW
    4. D.50 KW
    Show answer

    Answer: C. 25 KW

    AI explanation

    Analysis

    To find the power developed by the engine, we need to understand the relationship between power, force, and velocity. Power is defined as the rate of doing work, or the product of force and velocity (P=F×vP = F \times v).

    Concept
    1. Force (FF): According to Newton’s Second Law, F=maF = ma. Since the train starts from rest (u=0u = 0) and reaches a final velocity (v=25 ms−1v = 25 \text{ ms}^{-1}) in time (t=20 st = 20 \text{ s}), we first find the acceleration (aa): $a=v−uta = \frac{v - u}{t}$
    2. Power (PP): Since the velocity is changing, we use the average velocity (vavgv_{avg}) to calculate the power developed over that interval: $P=F×vavgP = F \times v_{avg}Where Where v_{avg} = \frac{u + v}{2}$
    Step-by-Step Solution

    Step 1: Calculate the acceleration (aa)

    a=25−020=2520=1.25 ms−2a = \frac{25 - 0}{20} = \frac{25}{20} = 1.25 \text{ ms}^{-2}

    Step 2: Calculate the Force (FF)

    F=m×aF = m \times a
    F=1600 kg×1.25 ms−2=2000 NF = 1600 \text{ kg} \times 1.25 \text{ ms}^{-2} = 2000 \text{ N}

    Step 3: Calculate the average velocity (vavgv_{avg})

    vavg=0+252=12.5 ms−1v_{avg} = \frac{0 + 25}{2} = 12.5 \text{ ms}^{-1}

    Step 4: Calculate the Power (PP)

    P=F×vavgP = F \times v_{avg}
    P=2000 N×12.5 ms−1=25,000 WattsP = 2000 \text{ N} \times 12.5 \text{ ms}^{-1} = 25,000 \text{ Watts}

    Step 5: Convert to Kilowatts (KW) Since 1000 W=1 KW1000 \text{ W} = 1 \text{ KW}:

    P=25,0001000=25 KWP = \frac{25,000}{1000} = 25 \text{ KW}
    Conclusion

    The power developed by the engine is 25 KW. This matches option C.

    Exam Tip

    When a question involves acceleration from rest, remember that the power developed is not constant. Always use the average velocity (vavg=v+u2v_{avg} = \frac{v+u}{2}) when calculating the power developed during a period of uniform acceleration. If you had used the final velocity (25 ms−125 \text{ ms}^{-1}) instead of the average, you would have arrived at 50 KW, which is a common distractor in JAMB questions!

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  37. 37.

    What quantity of heat is required to convert 20 g of ice at 0 ºC to water at the same temperature? (Specific latent heat of ice = 336 Jg−1^{-1})

    1. A.7.06 x 103^{3}J
    2. B.5.38 x 103^{3}J
    3. C.6.72 x 103^{3}J
    4. D.1.35 x 103^{3}J
    Show answer

    Answer: C. 6.72 x 103^{3}J

    AI explanation

    Analysis

    The question asks for the amount of heat energy required to change the state of a substance (ice to water) without a change in temperature. This is a classic phase change problem.

    Concept

    When a substance changes state (e.g., from solid to liquid) at a constant temperature, we use the formula for Specific Latent Heat:

    Q=mLQ = mL

    Where:

    • QQ = Quantity of heat energy (in Joules, J)
    • mm = Mass of the substance (in grams, g)
    • LL = Specific latent heat of fusion (in Jg⁻¹)
    Solution

    Step 1: Identify the given values

    • Mass (mm) = 20 g
    • Specific latent heat of fusion (LL) = 336 Jg⁻¹

    Step 2: Apply the formula

    Q=m×LQ = m \times L
    Q=20 g×336 Jg−1Q = 20 \text{ g} \times 336 \text{ Jg}^{-1}

    Step 3: Calculate the result

    Q=6720 JQ = 6720 \text{ J}

    Step 4: Convert to standard form To match the options provided, we express 6720 in scientific notation:

    6720=6.72×103 J6720 = 6.72 \times 10^{3} \text{ J}
    Conclusion

    Comparing our result to the given options, 6.72×103 J6.72 \times 10^{3} \text{ J} corresponds to option C.

    Exam Tip

    Always check the units! If the specific latent heat were given in J/kg, you would first need to convert the mass from grams to kilograms (divide by 1000). Since the units here were both in grams (Jg⁻¹ and g), you could multiply them directly without conversion.

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  38. 38.

    For a pear-shaped conductor shown above, the concentration of charge on the outside is highest at?

    1. A.X
    2. B.Z
    3. C.Y
    4. D.K
    Show answer

    Answer: C. Y

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  39. 39.

    A bar magnet is placed near and lying along the axis of a solenoid connected to a galvanometer. The pointer of the galvanometer shows no deflection when?

    1. A.the magnet is moved towards the stationary solenoid
    2. B.there is no relative motion
    3. C.the magnet is moved away from the stationary solenoid
    4. D.the solenoid is moved away from the stationary magnet
    Show answer

    Answer: B. there is no relative motion

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  40. 40.

    A magnet relay is a device used for?

    1. A.reading the magnitude of magnetic flux
    2. B.controlling another circuit carrying larger current
    3. C.turning in sports
    4. D.storing magnetic field
    Show answer

    Answer: B. controlling another circuit carrying larger current

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