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JAMB 2021

2021 JAMB Physics Past Questions and Answers

The 2021 JAMB Physics past questions with answers: 40 objective questions from the 2021 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.

    A given mass of gas has a pressure of 80 Nm−2^{-2} at a temperature of 47 C. If the temperature is reduced to 27 C with volume remaining constant, the new pressure is?

    1. A.46.0 Nm−2^{-2}
    2. B.75.0 Nm−2^{-2}
    3. C.80.0 Nm−2^{-2}
    4. D.85.3 Nm−2^{-2}
    Show answer

    Answer: B. 75.0 Nm−2^{-2}

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  2. 2.

    The equation of a wave traveling along the positive x-direction is given by; y = 0.25 x 10−3^{-3} sin (500t - 0.025x). Determine the angular velocity of the wave motion.

    1. A.0.25 x 10−3^{-3}rads−1^{-1}
    2. B.0.25 x 10−1^{-1}rads−1^{-1}
    3. C.5.00 x 102^{2}rads−1^{-1}
    4. D.2.50 x 103^{3}rads−1^{-1}
    Show answer

    Answer: C. 5.00 x 102^{2}rads−1^{-1}

    AI explanation

    1. Analyze the Question

    You are given the wave equation y=0.25×10−3sin⁡(500t−0.025x)y = 0.25 \times 10^{-3} \sin(500t - 0.025x) and asked to find the angular velocity (also known as angular frequency, denoted by ω\omega).

    2. Explain the Concept

    The standard equation for a progressive wave traveling in the positive x-direction is:

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

    Where:

    • AA is the amplitude.
    • ω\omega is the angular velocity (angular frequency) in rads−1\text{rads}^{-1}.
    • tt is the time.
    • kk is the wave number.
    • xx is the displacement.

    By comparing the given equation to the standard form, you can identify the value of ω\omega by looking at the coefficient of tt.

    3. Show the Solution

    Given equation:

    y=0.25×10−3sin⁡(500t−0.025x)y = 0.25 \times 10^{-3} \sin(500t - 0.025x)

    Standard equation:

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

    By direct comparison:

    • ω=500\omega = 500

    To express 500500 in standard scientific notation as shown in the options:

    500=5.00×100=5.00×102500 = 5.00 \times 100 = 5.00 \times 10^2

    Therefore, the angular velocity ω=5.00×102 rads−1\omega = 5.00 \times 10^2 \text{ rads}^{-1}.

    4. Identify the Answer

    Comparing our result to the options provided: A. 0.25×10−3 rads−10.25 \times 10^{-3} \text{ rads}^{-1} B. 0.25×10−1 rads−10.25 \times 10^{-1} \text{ rads}^{-1} C. 5.00×102 rads−15.00 \times 10^2 \text{ rads}^{-1} D. 2.50×103 rads−12.50 \times 10^3 \text{ rads}^{-1}

    The correct option is C.

    5. Tip

    When you see a wave equation, don't let the numbers intimidate you! Always write the standard equation (y=Asin⁡(ωt−kx)y = A \sin(\omega t - kx)) directly above or below the given equation. This makes it easy to "map" the values: the number attached to tt is always your angular velocity (ω\omega), and the number attached to xx is always your wave number (kk).

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  3. 3.

    0.5kg of water at 10ºC is completely converted to ice at 0ºC by extracting (88000) of heat from it. If the specific heat capacity of water is 4200jkg1^{1} Cº. Calculate the specific latent heat of fusion of ice.

    1. A.9.0kjkg−1^{-1}
    2. B.84.0kjkg−1^{-1}
    3. C.134.0kjkg−1^{-1}
    4. D.168.0kjkg−1^{-1}
    Show answer

    Answer: C. 134.0kjkg−1^{-1}

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  4. 4.

    A gas at a volume of V0_{0} in a container at pressure p0_{0} is compressed to one-fifth of its volume. What will be its pressure if the magnitude of its original temperature T is constant?

    1. A.p05\frac{p_{0}} {5}
    2. B.4p05\frac{4p_{0}}{5}
    3. C.p0_{0}
    4. D.5P0_{0}
    Show answer

    Answer: D. 5P0_{0}

    AI explanation

    1. Analyze the question

    We are given an initial state of a gas with volume V0V_0 and pressure p0p_0. The gas is compressed to a new volume which is 15\frac{1}{5} of the original volume. We are told the temperature TT remains constant. We need to find the new pressure.

    2. Explain the concept

    This problem involves Boyle’s Law. 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).

    The mathematical expression is:

    p1V1=p2V2p_1V_1 = p_2V_2

    Where:

    • p1p_1 and V1V_1 are the initial pressure and volume.
    • p2p_2 and V2V_2 are the final pressure and volume.
    3. Show the solution
    • Initial state: • Pressure = p0p_0 • Volume = V0V_0
    • Final state: • Pressure = p2p_2 (what we need to find) • Volume = 15V0\frac{1}{5}V_0

    Using the Boyle’s Law formula:

    p0×V0=p2×(V05)p_0 \times V_0 = p_2 \times \left(\frac{V_0}{5}\right)

    To solve for p2p_2, divide both sides by V05\frac{V_0}{5}:

    p2=p0×V0V05p_2 = \frac{p_0 \times V_0}{\frac{V_0}{5}}

    The V0V_0 terms cancel out:

    p2=p0×5p_2 = p_0 \times 5
    p2=5p0p_2 = 5p_0
    4. Identify the answer

    Comparing our result (5p05p_0) to the given options, it matches option D.

    5. Exam Tip

    Whenever you see "constant temperature" in a gas law question, immediately think of Boyle's Law. A quick mental shortcut: if the volume is divided by a number (like 5), the pressure must be multiplied by that same number because they are inversely proportional.

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  5. 5.

    A car of mass 800kg attains a speed of 25m/s in 20secs. The power developed in the engine is?

    1. A.1.25 x 104^{4}W
    2. B.2.50x 104^{4}W
    3. C.1.25 x 106^{6}W
    4. D.2.50 x 106^{6}W
    Show answer

    Answer: A. 1.25 x 104^{4}W

    AI explanation

    1. Analyze the Question

    We are given the mass of a car (m=800 kgm = 800\text{ kg}), its final velocity (v=25 m/sv = 25\text{ m/s}), and the time taken to reach that velocity (t=20 st = 20\text{ s}). We assume the car starts from rest (u=0 m/su = 0\text{ m/s}). We need to calculate the power developed by the engine.

    2. Explain the Concept

    Power is defined as the rate at which work is done or the rate at which energy is transferred.

    • Work Done (WW): In this case, the work done is equal to the change in kinetic energy of the car. • W=ΔK.E.=12mv2−12mu2W = \Delta K.E. = \frac{1}{2}mv^2 - \frac{1}{2}mu^2
    • Power (PP): Power is Work divided by time. • P=WtP = \frac{W}{t}
    3. Show the Solution

    Step 1: Calculate the Work Done (Kinetic Energy gained) Since the car starts from rest (u=0u = 0): W=12×m×v2W = \frac{1}{2} \times m \times v^2 W=12×800×(25)2W = \frac{1}{2} \times 800 \times (25)^2 W=400×625W = 400 \times 625 W=250,000 JoulesW = 250,000\text{ Joules} (or 2.5×105 J2.5 \times 10^5\text{ J})

    Step 2: Calculate the Power P=WtP = \frac{W}{t} P=250,00020P = \frac{250,000}{20} P=12,500 WattsP = 12,500\text{ Watts}

    Step 3: Convert to Standard Form 12,500=1.25×104 W12,500 = 1.25 \times 10^4\text{ W}

    4. Identify the Answer

    Comparing our result to the given options: A. 1.25×104 W1.25 \times 10^4\text{ W} B. 2.50×104 W2.50 \times 10^4\text{ W} C. 1.25×106 W1.25 \times 10^6\text{ W} D. 2.50×106 W2.50 \times 10^6\text{ W}

    The calculated value matches option A.

    5. Tip

    When solving power problems involving motion, always check if you are given force or velocity. If you have force and velocity, use P=FvP = Fv. If you have mass, velocity, and time (like in this question), calculating the change in kinetic energy and dividing by time is the most direct path to the answer. Don't forget to convert your final answer to standard form as required by JAMB!

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  6. 6.

    I. A liquid boils when its saturated vapor pressure is equal to the external pressure II. Dissolved substances in pure water lead to an increase in the boiling point. III. When the external pressure is increased, the boiling point increases. IV. Dissolved substances in pure water decreases the boiling point  Which of the above combinations are peculiarities of the boiling point of a liquid?

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

    Answer: A. I, II and III only

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  7. 7.

    Calculate the heat energy required to vaporize 50g of water initially at 80ºC if the specific heat capacity of water is 4.23jg−1^{-1}k−1^{-1} (specific latent heat of vaporization of water is 2260jg−1^{-1}

    1. A.530000J
    2. B.23200J
    3. C.17200J
    4. D.130000J
    Show answer

    Answer: B. 23200J

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  8. 8.

    A piece of substance of specific heat capacity 450Jkg−1^{-1}k1^{1} falls through a vertical distance of 20m from rest. Calculate the rise in temperature of the substance on hitting the ground when all its energies are converted into heat. [g = 10ms−2^{-2}]

    1. A.29\frac{2}{9}ºC
    2. B.49\frac{4}{9}ºC
    3. C.92\frac{9}{2}ºC
    4. D.94\frac{9}{4}ºC
    Show answer

    Answer: B. 49\frac{4}{9}ºC

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  9. 9.

    A ball of mass 0.5kg moving at 10ms−1^{-1} collides with another ball of equal mass at rest. If the two balls move off together after the impact, calculate their common velocity.

    1. A.0.2ms−1^{-1}
    2. B.0.5ms−1^{-1}
    3. C.5.0ms−1^{-1}
    4. D.5.5ms−1^{-1}
    Show answer

    Answer: C. 5.0ms−1^{-1}

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  10. 10.

    Particles of mass 10−2^{-2}kg is fixed to the tip of a fan blade which rotates with angular velocity of 100rad−1^{-1}. If the radius of the blade is 0.2m, the centripetal force is?

    1. A.2N
    2. B.20N
    3. C.200N
    4. D.400N
    Show answer

    Answer: B. 20N

    AI explanation

    Analysis

    To solve this problem, we need to calculate the centripetal force acting on a particle moving in a circular path. We are given:

    • Mass (mm) = 10−2 kg10^{-2} \text{ kg}
    • Angular velocity (ω\omega) = 100 rad/s100 \text{ rad/s}
    • Radius (rr) = 0.2 m0.2 \text{ m}
    Concept

    The centripetal force (FcF_c) is the force required to keep an object moving in a circular path. The formula relating centripetal force to angular velocity is:

    Fc=mω2rF_c = m \omega^2 r

    Where:

    • mm is the mass in kilograms (kg)
    • ω\omega is the angular velocity in radians per second (rad/s)
    • rr is the radius in meters (m)
    Solution
    1. Identify the variables: • m=10−2 kg=0.01 kgm = 10^{-2} \text{ kg} = 0.01 \text{ kg} • ω=100 rad/s\omega = 100 \text{ rad/s} • r=0.2 mr = 0.2 \text{ m}
    1. Substitute the values into the formula: $Fc=(0.01)×(100)2×(0.2)F_c = (0.01) \times (100)^2 \times (0.2)$
    1. Perform the calculation: • First, square the angular velocity: 1002=10,000100^2 = 10,000 • Now, multiply the terms: Fc=0.01×10,000×0.2F_c = 0.01 \times 10,000 \times 0.2 • 0.01×10,000=1000.01 \times 10,000 = 100 • 100×0.2=20100 \times 0.2 = 20

    The centripetal force is 20 N.

    Conclusion

    Comparing our result to the given options: A. 2N B. 20N C. 200N D. 400N

    The calculated value matches option B.

    Exam Tip

    When dealing with circular motion questions in JAMB, always check your units first! If the angular velocity were given in revolutions per minute (rpm), you would need to convert it to radians per second (rad/s\text{rad/s}) by multiplying by 2π60\frac{2\pi}{60} before plugging it into the formula. Also, remember that 10−210^{-2} is the same as 0.010.01; converting to decimals often makes the multiplication easier to handle without a calculator.

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  11. 11.

    If the stress on a wire is 107^{7}NM−2^{-2} and the wire is stretched from its original length of 10.00m to 10.05m. The young's modulus of the wire is?

    1. A.5.0 x 10−4^{-4}Nm−2^{-2}
    2. B.5.0 x 10−5^{-5}Nm−2^{-2}
    3. C.2.0 x 10−8^{-8}Nm−2^{-2}
    4. D.2.0 x 109^{9}Nm−2^{-2}
    Show answer

    Answer: D. 2.0 x 109^{9}Nm−2^{-2}

    AI explanation

    1. Analyze the question

    We are given:

    • Stress (σ\sigma): 107 Nm−210^7 \, \text{Nm}^{-2}
    • Original length (LL): 10.00 m10.00 \, \text{m}
    • New length (L′L'): 10.05 m10.05 \, \text{m}
    • Goal: Calculate the Young's Modulus (EE).
    2. Explain the concept

    Young's Modulus (EE) is defined as the ratio of Stress to Strain.

    • Stress (σ\sigma): Force per unit area (FA\frac{F}{A}).
    • Strain (ϵ\epsilon): The ratio of the change in length (ΔL\Delta L) to the original length (LL). • Strain=ΔLL\text{Strain} = \frac{\Delta L}{L}
    • Formula: E=StressStrain=σΔL/LE = \frac{\text{Stress}}{\text{Strain}} = \frac{\sigma}{\Delta L / L}
    3. Show the solution

    Step 1: Calculate the change in length (ΔL\Delta L)

    ΔL=L′−L\Delta L = L' - L
    ΔL=10.05 m−10.00 m=0.05 m\Delta L = 10.05 \, \text{m} - 10.00 \, \text{m} = 0.05 \, \text{m}

    Step 2: Calculate the Strain (ϵ\epsilon)

    Strain=ΔLL=0.0510.00\text{Strain} = \frac{\Delta L}{L} = \frac{0.05}{10.00}
    Strain=0.005=5×10−3\text{Strain} = 0.005 = 5 \times 10^{-3}

    Step 3: Calculate Young's Modulus (EE)

    E=StressStrainE = \frac{\text{Stress}}{\text{Strain}}
    E=1075×10−3E = \frac{10^7}{5 \times 10^{-3}}

    To simplify this, treat the numbers and powers of 10 separately:

    E=(15)×107−(−3)E = \left(\frac{1}{5}\right) \times 10^{7 - (-3)}
    E=0.2×1010E = 0.2 \times 10^{10}

    To express this in standard form:

    E=2.0×109 Nm−2E = 2.0 \times 10^9 \, \text{Nm}^{-2}
    4. Identify the answer

    Comparing our result to the options provided, the correct value is 2.0×109 Nm−22.0 \times 10^9 \, \text{Nm}^{-2}. This matches option D.

    5. Tip

    When dealing with Young's Modulus questions, always ensure your units are consistent (meters for length). If you see a very small strain, don't panic—the resulting Young's Modulus is usually a very large number, which is typical for materials like steel or copper.

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  12. 12.

    The lowest note emitted by a stretched string has a frequency of 40Hz. How many overtones are there between 40Hz and 180Hz?

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

    Answer: B. 3

    AI explanation

    Analysis

    To solve this, we need to understand the relationship between the fundamental frequency, harmonics, and overtones in a stretched string.

    Concept
    1. Fundamental Frequency (f0f_0): This is the lowest frequency produced by the string. In this case, f0=40 Hzf_0 = 40\text{ Hz}.
    2. Harmonics: These are integer multiples of the fundamental frequency (1f0,2f0,3f0,4f0,…1f_0, 2f_0, 3f_0, 4f_0, \dots).
    3. Overtones: These are the frequencies produced above the fundamental frequency. • The 1st overtone is the 2nd harmonic (2×f02 \times f_0). • The 2nd overtone is the 3rd harmonic (3×f03 \times f_0). • The nn-th overtone is the (n+1)(n+1)-th harmonic.
    Step-by-Step Solution
    • Step 1: Identify the frequencies of the harmonics. • Fundamental frequency (f0f_0): 40 Hz40\text{ Hz} • 1st overtone (2nd harmonic): 2×40 Hz=80 Hz2 \times 40\text{ Hz} = 80\text{ Hz} • 2nd overtone (3rd harmonic): 3×40 Hz=120 Hz3 \times 40\text{ Hz} = 120\text{ Hz} • 3rd overtone (4th harmonic): 4×40 Hz=160 Hz4 \times 40\text{ Hz} = 160\text{ Hz} • 4th overtone (5th harmonic): 5×40 Hz=200 Hz5 \times 40\text{ Hz} = 200\text{ Hz}
    • Step 2: Determine which overtones fall between 40Hz and 180Hz. • The overtones are 80 Hz80\text{ Hz}, 120 Hz120\text{ Hz}, and 160 Hz160\text{ Hz}. • All three of these values (80,120,16080, 120, 160) are greater than 40 Hz40\text{ Hz} and less than 180 Hz180\text{ Hz}. • The next overtone (200 Hz200\text{ Hz}) is greater than 180 Hz180\text{ Hz}, so we exclude it.
    • Step 3: Count the overtones. • There are exactly 3 overtones in the specified range.
    Conclusion

    There are 3 overtones (80Hz, 120Hz, and 160Hz) between 40Hz and 180Hz.

    Exam Tip

    Always remember the "n+1" rule: the nn-th overtone is always the (n+1)(n+1)-th harmonic. If you are ever confused, just list the multiples of the fundamental frequency and count everything after the first one!

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  13. 13.

    A ball of mass 0.1kg is thrown vertically upwards with a speed of 10ms−1^{-1} from the top of a tower 10m high. Neglecting air resistance, its total energy just before hitting the ground is? (Take g = 10ms−2^{-2})

    1. A.5J
    2. B.10J
    3. C.15J
    4. D.20J
    Show answer

    Answer: C. 15J

    AI explanation

    Analysis

    To solve this problem, we apply the Law of Conservation of Mechanical Energy. This law states that in the absence of air resistance, the total mechanical energy of an object remains constant throughout its motion. Therefore, the total energy at the top of the tower is equal to the total energy just before the ball hits the ground.

    Concept

    Total Mechanical Energy (ETE_T) is the sum of Kinetic Energy (K.E.K.E.) and Potential Energy (P.E.P.E.):

    ET=K.E.+P.E.E_T = K.E. + P.E.
    • Kinetic Energy (K.E.K.E.) = 12mv2\frac{1}{2}mv^2
    • Potential Energy (P.E.P.E.) = mghmgh

    Where:

    • mm = mass (0.1 kg)
    • vv = velocity (10 m/s)
    • gg = acceleration due to gravity (10 m/s²)
    • hh = height (10 m)
    Solution

    We calculate the total energy at the point of release (the top of the tower):

    1. Calculate Kinetic Energy (K.E.K.E.): $K.E.=12×0.1×(10)2K.E. = \frac{1}{2} \times 0.1 \times (10)^2$ $K.E.=0.5×0.1×100K.E. = 0.5 \times 0.1 \times 100$ $K.E.=5 JK.E. = 5\text{ J}$
    1. Calculate Potential Energy (P.E.P.E.): $P.E.=mghP.E. = mgh$ $P.E.=0.1×10×10P.E. = 0.1 \times 10 \times 10$ $P.E.=10 JP.E. = 10\text{ J}$
    1. Calculate Total Energy (ETE_T): $ET=K.E.+P.E.E_T = K.E. + P.E.$ $ET=5 J+10 JE_T = 5\text{ J} + 10\text{ J}$ $ET=15 JE_T = 15\text{ J}$

    Since energy is conserved, the total energy just before hitting the ground is the same as the total energy at the start.

    Conclusion

    The total energy of the ball is 15J. This matches option C.

    Exam Tip

    In physics problems involving "neglecting air resistance," always look for the point where you have all the necessary values (mass, height, and velocity) to calculate the total energy. Once you find the total energy at that point, you don't need to perform complex calculations for the final position—the energy remains the same!

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  14. 14.

    Which of the following instruments may be used to measure relative humidity?

    1. A.Hydrometer
    2. B.Manometer
    3. C.Hygrometer
    4. D.Hypsometer
    Show answer

    Answer: C. Hygrometer

    AI explanation

    Analysis

    The question asks for the specific scientific instrument used to determine the amount of water vapor present in the air, known as relative humidity.

    Concept Explanation

    To identify the correct instrument, we must distinguish between the functions of the devices listed:

    • Hydrometer: This is used to measure the relative density (or specific gravity) of liquids. It works on the principle of buoyancy.
    • Manometer: This is a device used to measure gas or liquid pressure. It typically consists of a U-shaped tube containing a liquid.
    • Hygrometer: This is the standard instrument used to measure the humidity of the air. Common types include the hair hygrometer and the wet-and-dry bulb hygrometer (psychrometer).
    • Hypsometer: This is used to calibrate thermometers or determine altitude by measuring the boiling point of a liquid at different pressures.
    Step-by-Step Solution
    1. Evaluate Option A: A hydrometer measures liquid density, not humidity. Incorrect.
    2. Evaluate Option B: A manometer measures pressure, not humidity. Incorrect.
    3. Evaluate Option C: A hygrometer is specifically designed to measure the moisture content (humidity) in the atmosphere. Correct.
    4. Evaluate Option D: A hypsometer measures boiling points to determine altitude. Incorrect.
    Exam Tip

    Don't let the similar-sounding names confuse you! Remember:

    • Hydro = Water/Liquid density (Hydrometer)
    • Hygro = Humidity (Hygrometer)
    • Hypso = Height/Altitude (Hypsometer)

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  15. 15.

    When the breaks in a car are applied, the frictional force on the tyres is?

    1. A.a disadvantage because it is in the direction of the motion of the car
    2. B.a disadvantage because it is in the opposite direction of the motion of the car
    3. C.an advantage because it is in the direction of the motion of the car
    4. D.an advantage because it is in the opposite direction of the motion of the car
    Show answer

    Answer: D. an advantage because it is in the opposite direction of the motion of the car

    AI explanation

    Analysis

    This question tests your understanding of friction and its role in daily mechanics, specifically regarding vehicle safety and control.

    Concept Explanation

    Friction is a force that opposes the relative motion between two surfaces in contact. In the context of a moving car:

    1. The Role of Friction: When you apply the brakes, the brake pads grip the wheels, and the tyres grip the road. This creates a frictional force between the tyres and the road surface.
    2. Direction: Because friction always acts to oppose motion, the frictional force generated by the road on the tyres acts in the opposite direction to the car's velocity.
    3. Advantage vs. Disadvantage: In this specific scenario, this force is an advantage. Without this opposing frictional force, the car would not be able to decelerate or come to a stop. It is the force that allows the car to lose kinetic energy and eventually stop safely.
    Step-by-Step Solution
    1. Identify the goal: The goal of applying brakes is to stop the car.
    2. Determine the force direction: To stop a forward-moving object, a force must be applied in the backward direction (opposite to the motion). Friction provides this force.
    3. Evaluate the nature of the force: Since the force achieves the desired outcome (stopping the car), it is classified as an advantage.
    4. Conclusion: The frictional force is an advantage because it acts in the opposite direction of the motion, effectively reducing the car's speed.
    Exam Strategy Tip

    Whenever you encounter questions about friction in exams, ask yourself: "Is this friction helping me achieve the intended motion or stop it?"

    • If it helps you move (like walking or a car accelerating), it is an advantage.
    • If it helps you stop (like braking), it is also an advantage.
    • If it causes unwanted wear and tear or heat (like in an engine), it is a disadvantage.

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  16. 16.

    The temperature gradient across a copper rod of thickness 0.02m, maintained at two temperature junctions of 20º and 80ºC respectively is?

    1. A.3.0 x 102^{2}km−1^{-1}
    2. B.3.0 x 103^{3}km−1^{-1}
    3. C.5.0 x 103^{3}km−1^{-1}
    4. D.3.0 x 104^{4}km−1^{-1}
    Show answer

    Answer: B. 3.0 x 103^{3}km−1^{-1}

    AI explanation

    1. Analyze the Question

    We are asked to calculate the temperature gradient across a copper rod. We are given:

    • Thickness of the rod (LL) = 0.02 m0.02 \, \text{m}
    • Temperature at the first junction (T1T_1) = 20∘C20^\circ\text{C}
    • Temperature at the second junction (T2T_2) = 80∘C80^\circ\text{C}
    2. Explain the Concept

    The temperature gradient is defined as the rate of change of temperature with respect to distance. It represents how much the temperature changes per unit length of the material.

    The formula is:

    Temperature Gradient=ΔTL\text{Temperature Gradient} = \frac{\Delta T}{L}

    Where:

    • ΔT\Delta T is the temperature difference (T2−T1T_2 - T_1)
    • LL is the thickness (or length) of the material
    3. Show the Solution

    Step 1: Calculate the temperature difference (ΔT\Delta T)

    ΔT=T2−T1\Delta T = T_2 - T_1
    ΔT=80∘C−20∘C=60∘C\Delta T = 80^\circ\text{C} - 20^\circ\text{C} = 60^\circ\text{C}

    Step 2: Apply the formula

    Temperature Gradient=600.02\text{Temperature Gradient} = \frac{60}{0.02}

    Step 3: Simplify the calculation To make the division easier, multiply both the numerator and the denominator by 100:

    Temperature Gradient=60002\text{Temperature Gradient} = \frac{6000}{2}
    Temperature Gradient=3000 K/m\text{Temperature Gradient} = 3000 \, \text{K/m}

    Step 4: Convert to standard form

    3000=3.0×103 K/m3000 = 3.0 \times 10^3 \, \text{K/m}

    (Note: In physics, a change in temperature of 1∘C1^\circ\text{C} is equivalent to a change of 1 K1 \, \text{K}, so the unit K/m\text{K/m} is correct.)

    4. Identify the Answer

    Comparing our result (3.0×103 K/m3.0 \times 10^3 \, \text{K/m}) with the given options, it matches Option B.

    5. Exam Tip

    When calculating gradients (whether temperature, velocity, or pressure), always ensure your units are consistent. If the thickness were given in centimeters, you would have to convert it to meters first to match the standard SI unit of K/m\text{K/m}. Don't let the decimal points confuse you—moving the decimal two places to the right for the denominator (0.02→20.02 \rightarrow 2) means you must also move the decimal two places for the numerator (60→600060 \rightarrow 6000).

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  17. 17.

    Which of the following is not a vector quantity?

    1. A.momentum
    2. B.force
    3. C.temperature
    4. D.displacement
    Show answer

    Answer: C. temperature

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  18. 18.

    The inner diameter of a test tube can be measured accurately using a?

    1. A.micrometer screw gauge
    2. B.pair of dividers
    3. C.meter rule
    4. D.pair of vernier calipers
    Show answer

    Answer: D. pair of vernier calipers

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  19. 19.

    If a sound wave goes from a cold air region to a hot air region, its wavelength will?

    1. A.increase
    2. B.decrease
    3. C.decrease then increase
    4. D.remain constant
    Show answer

    Answer: A. increase

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  20. 20.

    Which of the following is not correct about the molecules of a substance in a gaseous state. They?

    1. A.are in a constant state of motion
    2. B.have different speeds
    3. C.have a temperature which is measured by the average kinetic energy
    4. D.The collision between the gases is perfectly inelastic
    Show answer

    Answer: D. The collision between the gases is perfectly inelastic

    AI explanation

    Analysis of the Question

    This question tests your understanding of the Kinetic Theory of Gases. The Kinetic Theory makes several assumptions about the behavior of gas molecules to explain their physical properties. We need to identify which statement among the options is not a valid assumption of this theory.

    Concept Explanation

    The Kinetic Theory of Gases is based on these fundamental postulates:

    1. Motion: Gas molecules are in constant, random, and rapid motion.
    2. Speed: At any given temperature, molecules move at different speeds (a distribution of speeds).
    3. Temperature: The absolute temperature of a gas is directly proportional to the average kinetic energy of its molecules.
    4. Collisions: Collisions between gas molecules, and between molecules and the walls of the container, are perfectly elastic. This means there is no loss of kinetic energy during these collisions.
    5. Volume: The volume of the molecules themselves is negligible compared to the total volume of the gas.
    Step-by-Step Evaluation
    • Option A: "Are in a constant state of motion." This is correct according to the Kinetic Theory.
    • Option B: "Have different speeds." This is correct. Due to constant collisions, molecules constantly exchange energy, leading to a range of speeds (Maxwell-Boltzmann distribution).
    • Option C: "Have a temperature which is measured by the average kinetic energy." This is correct. The formula KEavg=32kTKE_{avg} = \frac{3}{2}kT shows this direct relationship.
    • Option D: "The collision between the gases is perfectly inelastic." This is incorrect. In physics, an inelastic collision involves a loss of kinetic energy (often converted to heat or deformation). If gas collisions were inelastic, the gas would eventually lose all its kinetic energy and settle, which contradicts the observed behavior of gases. Therefore, collisions must be perfectly elastic.
    Conclusion

    Since the question asks for the statement that is not correct, Option D is the right choice because it contradicts the fundamental postulate that gas collisions are perfectly elastic.

    Exam Tip: Whenever you see questions about the Kinetic Theory of Gases, always remember the "Elastic" rule. Think of gas molecules like tiny, perfect billiard balls that never lose energy when they hit each other or the walls of their container!

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  21. 21.

    If the frequency of an emitted x-ray is 1.6 x 1016^{16}Hz, the accelerating potential is?  [e = 1.6 x 10−19^{-19}J, h = 6.63 x 10-34^{34}Js]

    1. A.6630.0V
    2. B.663.0V
    3. C.66.3V
    4. D.6.6V
    Show answer

    Answer: C. 66.3V

    AI explanation

    1. Analyze the Question

    We are given the frequency (ff) of an emitted X-ray and asked to find the accelerating potential (VV) required to produce it. We are provided with the elementary charge (ee) and Planck's constant (hh).

    2. Explain the Concept

    In X-ray production, the kinetic energy gained by an electron accelerated through a potential difference VV is converted into the energy of the emitted X-ray photon. This is based on the principle of conservation of energy: Electrical Energy = Photon Energy

    eV=hfeV = hf

    Where:

    • ee = charge of an electron (1.6×10−19 C1.6 \times 10^{-19} \, \text{C})
    • VV = accelerating potential (in Volts)
    • hh = Planck's constant (6.63×10−34 Js6.63 \times 10^{-34} \, \text{Js})
    • ff = frequency of the X-ray (1.6×1016 Hz1.6 \times 10^{16} \, \text{Hz})
    3. Show the Solution

    To find the potential VV, we rearrange the formula:

    V=hfeV = \frac{hf}{e}

    Step 1: Substitute the given values into the equation:

    V=(6.63×10−34)×(1.6×1016)1.6×10−19V = \frac{(6.63 \times 10^{-34}) \times (1.6 \times 10^{16})}{1.6 \times 10^{-19}}

    Step 2: Simplify the expression: Notice that 1.61.6 appears in both the numerator and the denominator, so they cancel out:

    V=6.63×10−34×101610−19V = \frac{6.63 \times 10^{-34} \times 10^{16}}{10^{-19}}

    Step 3: Solve the powers of 10: Using the laws of indices (10a×10b=10a+b10^a \times 10^b = 10^{a+b} and 10a10b=10a−b\frac{10^a}{10^b} = 10^{a-b}):

    V=6.63×10−34+16−(−19)V = 6.63 \times 10^{-34 + 16 - (-19)}
    V=6.63×10−34+16+19V = 6.63 \times 10^{-34 + 16 + 19}
    V=6.63×101V = 6.63 \times 10^{1}
    V=66.3 VV = 66.3 \, \text{V}
    4. Identify the Answer

    Comparing our result to the given options, we find that 66.3V matches option C.

    5. Exam Tip

    When you see a calculation involving 1.6×10−191.6 \times 10^{-19} (the charge of an electron) and 1.6×10161.6 \times 10^{16} (or similar values) in a physics problem, always look for opportunities to cancel out the 1.61.6 before doing any heavy multiplication. It saves time and reduces the chance of making a decimal point error!

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  22. 22.

    In a series R-L-C circuit at resonance, the voltages across the resistor and the inductors are 30V and 40V respectively. What is the voltage across the capacitor?

    1. A.30V
    2. B.40V
    3. C.50V
    4. D.70V
    Show answer

    Answer: B. 40V

    AI explanation

    1. Analyze the Question

    We are given a series R-L-C circuit operating at resonance. We know the voltage across the resistor (VR=30VV_R = 30\text{V}) and the voltage across the inductor (VL=40VV_L = 40\text{V}). We need to find the voltage across the capacitor (VCV_C).

    2. Explain the Concept

    In a series R-L-C circuit, resonance occurs when the inductive reactance (XLX_L) is equal to the capacitive reactance (XCX_C).

    Mathematically:

    XL=XCX_L = X_C

    Since the same current (II) flows through all components in a series circuit, we use Ohm's Law (V=IRV = IR) to relate the voltages:

    I⋅XL=I⋅XCI \cdot X_L = I \cdot X_C
    VL=VCV_L = V_C

    At resonance, the voltage drop across the inductor is exactly equal in magnitude to the voltage drop across the capacitor. These two voltages are 180∘180^\circ out of phase, which is why they cancel each other out, leaving the total supply voltage equal to the voltage across the resistor (Vtotal=VRV_{total} = V_R).

    3. Show the Solution
    • Given: • VR=30VV_R = 30\text{V} • VL=40VV_L = 40\text{V}
    • Condition: The circuit is at resonance.
    • Principle: At resonance, VL=VCV_L = V_C.
    • Calculation: Since VL=40VV_L = 40\text{V} and VL=VCV_L = V_C, then: $VC=40VV_C = 40\text{V}$
    4. Identify the Answer

    The voltage across the capacitor must be 40V to satisfy the condition of resonance. This matches option B.

    5. Exam Tip

    Always remember the "Resonance Rule": At resonance, the inductive and capacitive effects cancel each other out. If you see a question about a series R-L-C circuit at resonance, immediately look for the equality between VLV_L and VCV_C or XLX_L and XCX_C. Don't let the resistor voltage distract you—it is only there to tell you the total voltage of the circuit!

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  23. 23.

    If the fraction of the atoms of a radioactive material left after 120 years is 1/64, what is the half-life of the material?

    1. A.24 years
    2. B.20 years
    3. C.10 years
    4. D.2 years
    Show answer

    Answer: B. 20 years

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  24. 24.

    A certain radioactive source emits radiation that was found to be deflected by both magnetic and electric fields. The radiation is?

    1. A.beta rays
    2. B.gamma rays
    3. C.x-rays
    4. D.ultra-violet rays
    Show answer

    Answer: A. beta rays

    AI explanation

    Analysis of the Question

    The question asks us to identify a type of radiation based on its behavior in magnetic and electric fields. We need to recall the properties of the three main types of radioactive emissions: alpha particles, beta particles, and gamma rays.

    Explanation of the Concept

    In physics, the deflection of radiation in fields depends on whether the particles carry an electric charge:

    • Alpha particles (α\alpha): These are positively charged helium nuclei. They are deflected by both magnetic and electric fields.
    • Beta particles (β\beta): These are high-speed electrons (negatively charged). Because they carry a charge, they are also deflected by both magnetic and electric fields.
    • Gamma rays (γ\gamma): These are electromagnetic waves (photons). They carry no electric charge and have no mass. Therefore, they are not deflected by magnetic or electric fields.
    • X-rays and Ultra-violet rays: These are also forms of electromagnetic radiation and are not deflected by these fields.
    Step-by-Step Solution
    1. Evaluate the options: • Gamma rays, X-rays, and Ultra-violet rays are all electromagnetic waves. They are neutral (uncharged), so they pass through electric and magnetic fields without being deflected. • Beta rays consist of electrons. Electrons are charged particles.
    2. Apply the principle: According to the Lorentz force law, a charged particle moving through a magnetic or electric field experiences a force that causes it to deflect. Since beta rays are charged, they will be deflected.
    3. Conclusion: Among the given options, only beta rays possess the necessary charge to be deflected by both magnetic and electric fields.
    Identify the Answer

    The correct option is A.

    Exam Tip

    Remember the "Charge Rule":

    • Charged (Alpha and Beta) = Deflected by fields.
    • Uncharged (Gamma, X-rays, Light) = Not deflected by fields. This simple rule will help you answer any question regarding the nature of radiation in fields!

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  25. 25.

    The inside portion of part of a hollow metal sphere of diameter 20cm is polished. The portion will therefore form a?

    1. A.concave mirror of focal length 5cm
    2. B.concave mirror of focal length 10cm
    3. C.convex mirror of focal length 5cm
    4. D.convex mirror of focal length 10cm
    Show answer

    Answer: A. concave mirror of focal length 5cm

    AI explanation

    1. Analyze the question

    We are given a hollow metal sphere with a diameter of 20 cm. We are told that the inside portion of this sphere is polished to act as a mirror. We need to determine the type of mirror formed and its focal length.

    2. Explain the concept
    • Mirror Type: A mirror is classified based on its reflecting surface. If the reflecting surface is the inner (caved-in) part of a sphere, it is a concave mirror. If the reflecting surface is the outer (bulging) part, it is a convex mirror. Since the inside is polished, it is a concave mirror.
    • Focal Length (ff): The focal length of a spherical mirror is exactly half of its radius of curvature (RR). • Formula: f=R2f = \frac{R}{2} • The radius of curvature (RR) is half of the diameter (DD). • Formula: R=D2R = \frac{D}{2}
    3. Show the solution
    • Step 1: Find the radius of curvature (RR). Given the diameter (DD) = 20 cm. R=D2=20 cm2=10 cmR = \frac{D}{2} = \frac{20\text{ cm}}{2} = 10\text{ cm}.
    • Step 2: Calculate the focal length (ff). Using the relationship f=R2f = \frac{R}{2}: f=10 cm2=5 cmf = \frac{10\text{ cm}}{2} = 5\text{ cm}.
    • Step 3: Conclusion. Since the inside is polished, it is a concave mirror with a focal length of 5 cm.
    4. Identify the answer

    Comparing our result to the given options, the correct choice is A.

    5. Exam Tip

    Always remember the "C-C-C" rule for mirrors: Concave mirrors have Caved-in reflecting surfaces. Also, never confuse the radius of curvature with the focal length; always check if the question gives you the diameter or the radius before dividing by 2!

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  26. 26.

    A solid weighs 10.00N in air, 6N when forcefully immersed in water, and 7.0N when fully immersed in a liquid, X. Calculate the relative density of the liquid X.

    1. A.53\frac{5}{3}
    2. B.43\frac{4}{3}
    3. C.34\frac{3}{4}
    4. D.710\frac{7}{10}
    Show answer

    Answer: C. 34\frac{3}{4}

    AI explanation

    Analysis

    To solve this problem, we need to apply Archimedes' Principle, which states that the upthrust (loss in weight) experienced by an object immersed in a fluid is equal to the weight of the fluid displaced.

    Concept

    The relative density (RD) of a liquid is defined as:

    RD=Weight of liquid displacedWeight of an equal volume of water displaced\text{RD} = \frac{\text{Weight of liquid displaced}}{\text{Weight of an equal volume of water displaced}}

    Since the object is fully immersed in both cases, the volume of liquid displaced is equal to the volume of the object. Therefore:

    1. Upthrust in water = Weight in air - Weight in water
    2. Upthrust in liquid X = Weight in air - Weight in liquid X

    The ratio of these upthrusts gives the relative density of the liquid.

    Step-by-Step Solution

    Step 1: Calculate the upthrust in water.

    • Weight in air = 10.0 N10.0\text{ N}
    • Weight in water = 6.0 N6.0\text{ N}
    • Upthrust in water = 10.0 N−6.0 N=4.0 N10.0\text{ N} - 6.0\text{ N} = 4.0\text{ N}

    Step 2: Calculate the upthrust in liquid X.

    • Weight in air = 10.0 N10.0\text{ N}
    • Weight in liquid X = 7.0 N7.0\text{ N}
    • Upthrust in liquid X = 10.0 N−7.0 N=3.0 N10.0\text{ N} - 7.0\text{ N} = 3.0\text{ N}

    Step 3: Calculate the relative density of liquid X.

    RD=Upthrust in liquid XUpthrust in water\text{RD} = \frac{\text{Upthrust in liquid X}}{\text{Upthrust in water}}
    RD=3.04.0=34\text{RD} = \frac{3.0}{4.0} = \frac{3}{4}
    Conclusion

    Comparing our result to the given options, we find that the calculated value matches option C.

    Exam Tip

    Always remember that "Relative Density" is a ratio of weights (or upthrusts). If you ever get a value greater than 1 for a liquid that is less dense than water (like oil), double-check your subtraction! In this case, since the object weighed more in liquid X (7N7\text{N}) than in water (6N6\text{N}), liquid X must be less dense than water, so your answer must be less than 1.

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  27. 27.

    An astronomical telescope is said to be in normal adjustment when the?

    1. A.eye is accommodated
    2. B.focal length of an object lens is longer than that of eye piece
    3. C.final image is at the near point of eye
    4. D.final image is at infinity
    Show answer

    Answer: D. final image is at infinity

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  28. 28.

    Two bodies have masses in the ratio3:1. They experience forces which impart to them, acceleration in the ratio 2:9 respectively. Find the ratio of forces the masses experienced

    1. A.1:4
    2. B.2:1
    3. C.2:3
    4. D.2:5
    Show answer

    Answer: C. 2:3

    AI explanation

    Analysis

    To solve this problem, we need to use Newton’s Second Law of Motion, which relates force, mass, and acceleration. The formula is: F=m×aF = m \times a Where:

    • FF = Force
    • mm = Mass
    • aa = Acceleration
    Concept

    When comparing two bodies, we can express the ratio of their forces as: F1F2=m1×a1m2×a2\frac{F_1}{F_2} = \frac{m_1 \times a_1}{m_2 \times a_2}

    We are given:

    • Ratio of masses (m1:m2m_1 : m_2) = 3:13 : 1
    • Ratio of accelerations (a1:a2a_1 : a_2) = 2:92 : 9
    Step-by-Step Solution
    1. Set up the ratio formula: F1F2=(m1m2)×(a1a2)\frac{F_1}{F_2} = \left( \frac{m_1}{m_2} \right) \times \left( \frac{a_1}{a_2} \right)
    1. Substitute the given values: F1F2=(31)×(29)\frac{F_1}{F_2} = \left( \frac{3}{1} \right) \times \left( \frac{2}{9} \right)
    1. Perform the multiplication: F1F2=3×21×9\frac{F_1}{F_2} = \frac{3 \times 2}{1 \times 9} F1F2=69\frac{F_1}{F_2} = \frac{6}{9}
    1. Simplify the fraction: Divide both the numerator and the denominator by their greatest common divisor, which is 3: 6÷39÷3=23\frac{6 \div 3}{9 \div 3} = \frac{2}{3}

    The ratio of the forces is 2:3.

    Conclusion

    Comparing our result to the options provided, we see that it matches option C.

    Exam Tip: When dealing with ratio problems in Physics, always write down the formula first and group the ratios together. It prevents simple arithmetic errors and keeps your work organized. Don't let the "respectively" in the question confuse you—it simply means the first value in the mass ratio corresponds to the first value in the acceleration ratio.

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  29. 29.

    A lead bullet of mass 0.05kg is fired with a velocity of 200ms−1^{-1} into a block of mass 0.95kg. Given that the lead block can move freely, the final kinetic energy after impact is?

    1. A.50J
    2. B.100J
    3. C.150J
    4. D.200J
    Show answer

    Answer: A. 50J

    AI explanation

    Analysis

    This is a classic Inelastic Collision problem. In this scenario, the bullet embeds itself into the block, and they move together as a single unit after the impact. We need to use the Law of Conservation of Linear Momentum to find the final velocity, and then calculate the kinetic energy of the combined mass.

    Concept
    1. Conservation of Momentum: The total momentum before impact equals the total momentum after impact. $m1u1+m2u2=(m1+m2)vm_1u_1 + m_2u_2 = (m_1 + m_2)v$ Where: • m1=0.05 kgm_1 = 0.05\text{ kg} (mass of bullet) • u1=200 ms−1u_1 = 200\text{ ms}^{-1} (velocity of bullet) • m2=0.95 kgm_2 = 0.95\text{ kg} (mass of block) • u2=0 ms−1u_2 = 0\text{ ms}^{-1} (block is initially at rest) • v=final velocity of the combined massv = \text{final velocity of the combined mass}
    1. Kinetic Energy Formula: K.E.=12mv2K.E. = \frac{1}{2}mv^2
    Step-by-Step Solution

    Step 1: Find the final velocity (vv) Using the conservation of momentum:

    (0.05×200)+(0.95×0)=(0.05+0.95)×v(0.05 \times 200) + (0.95 \times 0) = (0.05 + 0.95) \times v
    10+0=1.0×v10 + 0 = 1.0 \times v
    v=10 ms−1v = 10\text{ ms}^{-1}

    Step 2: Calculate the final kinetic energy Now, use the combined mass (M=m1+m2=1.0 kgM = m_1 + m_2 = 1.0\text{ kg}) and the final velocity (v=10 ms−1v = 10\text{ ms}^{-1}):

    K.E.=12×M×v2K.E. = \frac{1}{2} \times M \times v^2
    K.E.=12×1.0×(10)2K.E. = \frac{1}{2} \times 1.0 \times (10)^2
    K.E.=0.5×100K.E. = 0.5 \times 100
    K.E.=50 JK.E. = 50\text{ J}
    Conclusion

    The final kinetic energy of the system after the impact is 50 Joules.

    Exam Tip

    In collision problems, always remember that while momentum is conserved, kinetic energy is usually lost (converted into heat or sound) during an inelastic collision. If you calculate the initial kinetic energy (0.5×0.05×2002=1000 J0.5 \times 0.05 \times 200^2 = 1000\text{ J}) and compare it to the final kinetic energy (50 J50\text{ J}), you will see a significant loss, which confirms the collision was inelastic.

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  30. 30.

    A source of sound produces waves in air of wavelength 1.65m. If the speed of sound in air is 330ms−1^{-1}, the period of vibration in air is?

    1. A.200
    2. B.0.005
    3. C.0.5
    4. D.0.02
    Show answer

    Answer: B. 0.005

    AI explanation

    Analysis

    To solve this problem, we need to relate the speed of sound, the wavelength, and the period of vibration.

    Concept

    The relationship between the speed of a wave (vv), its frequency (ff), and its wavelength (λ\lambda) is given by the formula:

    v=fλv = f \lambda

    We also know that frequency (ff) is the reciprocal of the period (TT):

    f=1Tf = \frac{1}{T}

    By substituting the second equation into the first, we get the relationship between speed, wavelength, and period:

    v=λTv = \frac{\lambda}{T}

    Rearranging this to solve for the period (TT):

    T=λvT = \frac{\lambda}{v}
    Step-by-Step Solution
    1. Identify the given values: • Wavelength (λ\lambda) = 1.65 m1.65 \, \text{m} • Speed of sound (vv) = 330 ms−1330 \, \text{ms}^{-1}
    1. Apply the formula: $T=1.65330T = \frac{1.65}{330}$
    1. Calculate the result: • To make the division easier, you can write 1.651.65 as 165100\frac{165}{100}: $T=165100×330T = \frac{165}{100 \times 330}$ • Since 165165 is half of 330330 (165×2=330165 \times 2 = 330): $T=1100×2T = \frac{1}{100 \times 2}$ $T=1200T = \frac{1}{200}$ $T=0.005 sT = 0.005 \, \text{s}$
    Conclusion

    The period of vibration is 0.0050.005 seconds. This matches option B.

    Exam Tip

    Always check your units before calculating. In JAMB Physics, speed is usually in ms−1\text{ms}^{-1} and wavelength in meters (m\text{m}), which gives the period in seconds (s\text{s}). If you ever forget the formula, remember that Speed = Distance / Time. In one period (TT), a wave travels exactly one wavelength (λ\lambda). Therefore, v=λ/Tv = \lambda / T.

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  31. 31.

    The motion of a body is simple harmonic if the?

    1. A.acceleration is always directed towards a fixed point
    2. B.path of motion is a straight line
    3. C.acceleration is proportional to the square of the distance from a fixed point
    4. D.acceleration is constant and directed towards a fixed point
    Show answer

    Answer: A. acceleration is always directed towards a fixed point

    AI explanation

    Analysis of the Question

    The question asks for the fundamental condition that defines Simple Harmonic Motion (SHM). To answer this, we must look at the mathematical and physical definition of SHM.

    Concept Explanation

    Simple Harmonic Motion (SHM) is a specific type of periodic motion where a body oscillates back and forth about a fixed equilibrium position.

    The defining characteristic of SHM is expressed by the mathematical relationship: a∝−xa \propto -x

    Where:

    • aa is the acceleration of the body.
    • xx is the displacement of the body from the fixed equilibrium point.
    • The negative sign (−-) indicates that the acceleration is always directed towards the equilibrium point (the fixed point), opposing the displacement.
    Step-by-Step Solution
    1. Evaluate Option A: In SHM, the acceleration is directly proportional to the displacement and is always directed towards the equilibrium point. This matches the definition perfectly.
    2. Evaluate Option B: While many SHM examples (like a simple pendulum or a mass on a spring) move in a straight line or arc, simply moving in a straight line does not make a motion "simple harmonic." Uniform velocity in a straight line is not SHM.
    3. Evaluate Option C: This is incorrect. Acceleration is proportional to the first power of the distance (displacement), not the square of the distance.
    4. Evaluate Option D: This describes uniform acceleration (like an object in free fall), not SHM. In SHM, acceleration is not constant; it changes continuously as the displacement changes.
    Conclusion

    Based on the definition of SHM, the acceleration must be directed towards a fixed point and be proportional to the displacement from that point. Option A correctly identifies the directional requirement of this motion.

    Exam Tip

    Whenever you see a question about SHM, remember the "Hooke’s Law" connection: F=−kxF = -kx. Since F=maF = ma, then ma=−kxma = -kx, which means a=−(k/m)xa = -(k/m)x. This proves that acceleration is always proportional to displacement and directed towards the center (the negative sign). Keep this formula in mind to eliminate distractors!

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  32. 32.

    A man will exert the greatest pressure when he?

    1. A.lies flat on his back
    2. B.lies on his belly
    3. C.stands on both feet
    4. D.stands on the toes of one foot
    Show answer

    Answer: D. stands on the toes of one foot

    AI explanation

    Analysis

    The question asks us to identify the condition under which a man exerts the greatest pressure. To solve this, we must look at the physical relationship between force, area, and pressure.

    Concept: Pressure

    In physics, Pressure (PP) is defined as the force (FF) applied perpendicularly per unit area (AA). The formula is:

    P=FAP = \frac{F}{A}

    From this formula, we can observe two things:

    1. Force (FF): In this scenario, the force is the man's weight, which remains constant regardless of his position.
    2. Area (AA): Pressure is inversely proportional to the area. This means that as the area of contact decreases, the pressure increases. To exert the greatest pressure, the man must minimize the area of contact with the ground.
    Step-by-Step Solution
    1. Analyze the options based on contact area: • Lying flat (on back or belly): The contact area is very large (the entire surface area of the body). This results in the lowest pressure. • Standing on both feet: The contact area is the surface area of two feet. This results in moderate pressure. • Standing on the toes of one foot: The contact area is extremely small (just the tips of the toes on one foot).
    1. Apply the principle: Since the man's weight (Force) is constant, the smallest area of contact will produce the highest pressure. Standing on the toes of one foot provides the smallest possible surface area among the given choices.
    Conclusion

    Because the area of contact is minimized when standing on the toes of one foot, the pressure exerted is at its maximum.

    The correct option is D.

    Exam Tip

    Whenever you see a question about pressure, remember the "High Heels vs. Flat Shoes" analogy. A person wearing high heels exerts more pressure on the floor than someone wearing flat shoes because the weight is concentrated on a much smaller surface area (the heel tip). Always look for the option that reduces the surface area to the smallest possible size!

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  33. 33.

    The slope of the straight line displacement-time graph indicates?

    1. A.distance traveled
    2. B.uniform velocity
    3. C.uniform acceleration
    4. D.uniform speed
    Show answer

    Answer: B. uniform velocity

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  34. 34.

    Calculate the mass of ice that would melt when 2kg of copper is quickly transferred from boiling water to a block of ice without heat loss (specific heat capacity of copper = 400Jkg1^{1}k−1^{-1}, latent heat of fusion of ice = 3.3 x 105^{5}Jkg−1^{-1})

    1. A.833\frac{8}{33}kg
    2. B.3.380\frac{3.3}{80}kg
    3. C.8033\frac{80}{33}kg
    4. D.3.38\frac{3.3}{8}kg
    Show answer

    Answer: A. 833\frac{8}{33}kg

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  35. 35.

    A 2H inductor has negligible resistance and is connected to a 50π\frac{50}{\pi} Hz A.C supply. The reactance of the inductor is?

    1. A.200Ω\Omega
    2. B.50Ω\Omega
    3. C.100π\frac{100}{\pi}
    4. D.25πΩ\frac{25}{\pi \Omega}
    Show answer

    Answer: A. 200Ω\Omega

    AI explanation

    1. Analyze the Question

    We are given an inductor with an inductance (LL) of 2 H2\text{ H} connected to an A.C. supply with a frequency (ff) of 50π Hz\frac{50}{\pi}\text{ Hz}. We need to calculate the inductive reactance (XLX_L).

    2. Explain the Concept

    In an A.C. circuit, an inductor opposes the flow of current. This opposition is called inductive reactance (XLX_L). The formula to calculate it is:

    XL=2πfLX_L = 2\pi f L

    Where:

    • XLX_L is the inductive reactance measured in Ohms (Ω\Omega).
    • π\pi is the constant (approximately 3.142).
    • ff is the frequency of the supply in Hertz (Hz).
    • LL is the inductance in Henrys (H).
    3. Show the Solution

    Given:

    • L=2 HL = 2\text{ H}
    • f=50π Hzf = \frac{50}{\pi}\text{ Hz}

    Substitute these values into the formula:

    XL=2×π×f×LX_L = 2 \times \pi \times f \times L
    XL=2×π×(50π)×2X_L = 2 \times \pi \times \left( \frac{50}{\pi} \right) \times 2

    Now, simplify the expression:

    • The π\pi in the numerator and the π\pi in the denominator cancel each other out:
    XL=2×50×2X_L = 2 \times 50 \times 2
    XL=100×2X_L = 100 \times 2
    XL=200ΩX_L = 200\Omega
    4. Identify the Answer

    Comparing our result of 200Ω200\Omega with the given options, it matches Option A.

    5. Exam Tip

    When dealing with A.C. circuits in JAMB Physics, always watch out for the π\pi in the frequency. Often, the examiners include it specifically so that it cancels out with the π\pi in the reactance formula (2πfL2\pi fL). If you see π\pi in the frequency, don't rush to convert it to 3.142; keep it as a symbol and look for the cancellation!

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  36. 36.

    A man stands 4m in front of a plane mirror. If the mirror is moved 1m towards the man, the distance between him and his new image is?

    1. A.3m
    2. B.5m
    3. C.6m
    4. D.10m
    Show answer

    Answer: C. 6m

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  37. 37.

    The velocities of light in air and glass are 3.0 x 108^8ms−1^{-1} and 2.0 x 108^8ms−1^{-1} respectively. If the angle of refraction is 30º, the sine of the angle of incidence is?

    1. A.0.33
    2. B.0.50
    3. C.0.67
    4. D.0.75
    Show answer

    Answer: D. 0.75

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  38. 38.

    A boy standing some distance from the foot of a tall cliff claps his hands and hears an echo 0.5s later. If the speed of sound is 340ms−1^{-1}, how far is he from the cliff?

    1. A.680m
    2. B.170m
    3. C.34m
    4. D.85m
    Show answer

    Answer: D. 85m

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  39. 39.

    Which of the units of the following physical quantities are derived? I. Area II. Thrust III. Pressure IV. Mass

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

    Answer: B. I, II, and III only

    AI explanation

    To solve this, we need to distinguish between Base Quantities and Derived Quantities in Physics.

    1. Analyze the Concepts
    • Base Quantities: These are fundamental physical quantities that cannot be defined in terms of other physical quantities. There are seven base quantities in the SI system: Length, Mass, Time, Electric Current, Temperature, Luminous Intensity, and Amount of Substance.
    • Derived Quantities: These are quantities that are expressed in terms of the base quantities through mathematical relationships (formulas).
    2. Evaluate the Given Quantities
    • I. Area: Area is calculated as Length×LengthLength \times Length (L2L^2). Since it is derived from length, it is a derived quantity.
    • II. Thrust: Thrust is a type of force. According to Newton's Second Law, Force=mass×accelerationForce = mass \times acceleration (M×LT−2M \times LT^{-2}). Since it is derived from mass, length, and time, it is a derived quantity.
    • III. Pressure: Pressure is defined as Force/AreaForce / Area. Since both Force and Area are derived, Pressure is also a derived quantity.
    • IV. Mass: Mass is one of the seven fundamental SI base quantities. Therefore, it is not a derived quantity.
    3. Conclusion

    Based on the analysis:

    • I (Area), II (Thrust), and III (Pressure) are derived.
    • IV (Mass) is base.

    Therefore, the quantities that are derived are I, II, and III only.

    4. Exam Tip

    A simple way to remember this is to look at the units. If the unit is a combination of base units (like m2m^2, kg⋅m/s2kg \cdot m/s^2, or N/m2N/m^2), it is derived. If the unit is one of the standard seven (like kgkg, mm, or ss), it is a base quantity.

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  40. 40.

    When the temperature of a liquid increases, its surface tension

    1. A.decreases
    2. B.increases
    3. C.remains constant
    4. D.increases then decreases
    Show answer

    Answer: A. decreases

    AI explanation

    Analysis of the Question

    This question tests your understanding of the molecular behavior of liquids and the concept of surface tension in relation to thermal energy.

    Concept Explanation

    Surface tension is the property of a liquid surface that allows it to resist an external force, caused by the cohesive forces between liquid molecules.

    Think of it this way: molecules at the surface of a liquid are pulled inward by the molecules beneath them. This creates a "skin" on the surface. When you increase the temperature of a liquid, you are providing kinetic energy to the molecules. As the molecules move faster and vibrate more vigorously, the cohesive forces (the "attraction" holding them together) are weakened. Because these cohesive forces are responsible for surface tension, weakening them leads to a reduction in surface tension.

    Step-by-Step Solution
    1. Identify the relationship: Surface tension is directly dependent on the strength of the cohesive forces between molecules.
    2. Apply the effect of heat: Increasing the temperature increases the average kinetic energy of the molecules.
    3. Observe the result: The increased kinetic energy allows molecules to overcome the cohesive forces more easily, causing the liquid to expand and the surface tension to drop.
    4. Conclusion: As temperature rises, the cohesive forces weaken, and therefore, the surface tension decreases.
    Correct Option

    The correct option is A.

    Exam Tip

    To remember this easily, think of hot water vs. cold water. Hot water is a better cleaning agent than cold water because its lower surface tension allows it to "wet" surfaces better and penetrate fabrics more easily. Therefore, Heat = Higher Temperature = Lower Surface Tension.

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