2024 JAMB Physics Past Questions and Answers

Questions 1–63

1. 1.

   The efficiency of a cell with internal resistance of 2$\Omega$ supply current to a 6$\Omega$ resistor is

   1. A.25%
   2. B.50%
   3. C.65%
   4. D.75%

   Show answer

   Answer: D. 75%

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2. 2.

   Two capacitors of 0.0003μF and 0.0006μF are connected in series, find their combined capacitance.

   1. A.0.0009μF
   2. B.0.0002μF
   3. C.0.0005μF
   4. D.0.0001μF

   Show answer

   Answer: B. 0.0002μF

   AI explanation

   Analysis

   To find the combined capacitance of capacitors connected in series, we use the reciprocal formula. This is similar to how resistors are calculated when connected in parallel.

   Concept

   When capacitors are connected in series, the total capacitance ($C_T$) is given by the formula:

   $\frac{1}{C_T} = \frac{1}{C_1} + \frac{1}{C_2}$

   Alternatively, for two capacitors, you can use the product-over-sum rule:

   $C_T = \frac{C_1 \times C_2}{C_1 + C_2}$

   Solution

   Given:

   • $C_1 = 0.0003 \, \mu\text{F}$
   • $C_2 = 0.0006 \, \mu\text{F}$

   Using the product-over-sum formula:

   $C_T = \frac{0.0003 \times 0.0006}{0.0003 + 0.0006}$

   1. Calculate the numerator: $0.0003 \times 0.0006 = 0.00000018$

   2. Calculate the denominator: $0.0003 + 0.0006 = 0.0009$

   3. Divide the results: $$C_T = \frac{0.00000018}{0.0009}$$To make this easier, move the decimal points:$$C_T = \frac{1.8 \times 10^{-7}}{9 \times 10^{-4}}$$ $$C_T = 0.2 \times 10^{-3} = 0.0002 \, \mu\text{F}$$

   Conclusion

   The combined capacitance is $0.0002 \, \mu\text{F}$. This matches option B.

   Exam Tip

   Always remember: When capacitors are in series, the total capacitance is always smaller than the smallest individual capacitor in the circuit. Since $0.0002 < 0.0003$, your answer is logically consistent!

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3. 3.

   What is the least possible error encountered when taking measurement with a metre rule?

   1. A.1.1mm
   2. B.0.5mm
   3. C.0.2mm
   4. D.0.1mm

   Show answer

   Answer: B. 0.5mm

   AI explanation

   Analysis

   The question asks for the "least possible error" (also known as the uncertainty or precision) when using a standard metre rule. In physics, the uncertainty of a measuring instrument is generally taken as half of its smallest scale division.

   Concept: Precision of Measuring Instruments

   A standard metre rule is calibrated in centimetres (cm) and millimetres (mm).

   • The smallest marking on a metre rule is 1 mm (or 0.1 cm).
   • When you take a measurement, you can typically estimate to the nearest half of the smallest division (e.g., if the object falls between 12 mm and 13 mm, you might estimate it as 12.5 mm).
   • Therefore, the uncertainty (least possible error) is calculated as: $$\text{Uncertainty} = \frac{1}{2} \times (\text{Smallest scale division})$$

   Step-by-Step Solution

   1. Identify the smallest division: The smallest division on a metre rule is 1 mm.
   2. Apply the uncertainty rule: The least possible error is half of the smallest division.
   3. Calculate: $$\text{Error} = \frac{1 \text{ mm}}{2} = 0.5 \text{ mm}$$

   Conclusion

   The least possible error when using a metre rule is 0.5 mm. This represents the limit of precision for the instrument.

   Exam Tip

   Always remember the "Half-Division Rule" for analogue instruments:

   • Metre Rule: Smallest division = 1 mm $\rightarrow$ Uncertainty = 0.5 mm.
   • Vernier Caliper: Smallest division = 0.1 mm $\rightarrow$ Uncertainty = 0.05 mm.
   • Micrometer Screw Gauge: Smallest division = 0.01 mm $\rightarrow$ Uncertainty = 0.005 mm.

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4. 4.

   If a body in linear motion changes from point P to Q, the motion is

   1. A.Translational
   2. B.Rotational
   3. C.Simple harmonic
   4. D.Circular

   Show answer

   Answer: A. Translational

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5. 5.

   Two tuning forks of frequencies 6Hz and 4Hz respectively are sounded together. The beat frequency is

   1. A.2Hz
   2. B.5Hz
   3. C.8Hz
   4. D.10Hz

   Show answer

   Answer: A. 2Hz

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6. 6.

   What will be the weight of a man of mass 60kg standing in a lift if the lift is descending vertically at 3ms$^2$?

   1. A.780N
   2. B.546N
   3. C.660N
   4. D.420N

   Show answer

   Answer: D. 420N

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7. 7.

   The distance between two successive crests of a water wave is 0.25m. If a particle on the surface of the water makes four complete vertical oscillations in one second. Calculate the speed of the wave.

   1. A.4ms$^{-1}$
   2. B.3ms$^{-1}$
   3. C.2ms$^{-1}$
   4. D.1ms$^{-1}$

   Show answer

   Answer: D. 1ms$^{-1}$

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8. 8.

   Electrolysis can be investigated using

   1. A.Voltmeter
   2. B.Ammeter
   3. C.Galvanometer
   4. D.Voltameter

   Show answer

   Answer: D. Voltameter

   AI explanation

   1. Analyze the Question

   The question asks for the specific apparatus used to investigate or perform the process of electrolysis. You need to distinguish between measuring instruments and the actual vessel where the chemical reaction occurs.

   2. Explain the Concept

   • Electrolysis is the process of using an electric current to drive a non-spontaneous chemical reaction. This process requires a container to hold the electrolyte (the substance being decomposed) and the electrodes (the conductors through which current enters or leaves the electrolyte).
   • Voltameter (or Electrolytic Cell): This is the vessel or apparatus designed specifically for electrolysis. It contains the electrolyte and the electrodes.
   • Voltmeter: This is an instrument used to measure the potential difference (voltage) between two points in an electrical circuit.
   • Ammeter: This is an instrument used to measure the current flowing through a circuit.
   • Galvanometer: This is a sensitive instrument used to detect and measure small electric currents.

   3. Show the Solution

   • To investigate electrolysis, you need a setup that allows current to pass through a liquid (electrolyte).
   • While an ammeter and voltmeter are used in the circuit to monitor the current and voltage during the experiment, they are measuring instruments, not the apparatus where the electrolysis itself takes place.
   • The voltameter is the specific name for the electrolytic cell used in laboratory experiments to study the decomposition of substances by electricity.

   Note: Be careful not to confuse "Voltameter" with "Voltmeter." They sound similar, but they serve completely different purposes.

   4. Identify the Answer

   The correct option is D.

   5. Exam Tip

   A simple way to remember this is:

   • Voltmeter = Measures Volts (Potential difference).
   • Voltameter = A Vessel for electrolysis (think of the 'a' as standing for the apparatus).

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9. 9.

   Find the value of a capacitor with voltage 5V and 30C.

   1. A.7f
   2. B.6f
   3. C.15f
   4. D.0.17f

   Show answer

   Answer: B. 6f

   AI explanation

   Analysis

   To solve this problem, we need to determine the capacitance ($C$) of a capacitor given the charge ($Q$) stored in it and the potential difference (voltage, $V$) across it.

   Concept

   The relationship between charge, capacitance, and voltage is defined by the fundamental formula for a capacitor:

   $Q = C \times V$

   Where:

   • $Q$ is the charge measured in Coulombs (C).
   • $C$ is the capacitance measured in Farads (F).
   • $V$ is the potential difference measured in Volts (V).

   To find the capacitance, we rearrange the formula to make $C$ the subject:

   $C = \frac{Q}{V}$

   Step-by-Step Solution

   1. Identify the given values: • Charge ($Q$) = $30\text{ C}$ • Voltage ($V$) = $5\text{ V}$

   2. Apply the formula: $$C = \frac{30\text{ C}}{5\text{ V}}$$

   3. Calculate the result: $$C = 6\text{ F}$$

   Conclusion

   The calculated capacitance is $6\text{ F}$. This matches option B.

   Exam Tip

   When dealing with capacitor problems, always remember the triangle method: put $Q$ at the top, and $C$ and $V$ at the bottom. If you need to find $C$, cover it up, and you are left with $Q$ over $V$. This simple trick helps you avoid mistakes under exam pressure!

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10. 10.

    An object is placed 25cm in front of a convex mirror has its image formed 5cm behind the mirror. what is the focal length of the convex mirror

    1. A.8.20cm
    2. B.6.25cm
    3. C.5.60cm
    4. D.4.50cm

    Show answer

    Answer: B. 6.25cm

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11. 11.

    Calculate the value of electric field intensity due to a charge of 4μC if the force due to the charge is 8N

    1. A.2.0 x 10$^6$NC$^{-1}$
    2. B.3.0 x 10$^6$NC$^{-1}$
    3. C.4.0 x 10$^6$NC$^{-1}$
    4. D.8.0 x 10$^6$NC$^{-1}$

    Show answer

    Answer: A. 2.0 x 10$^6$NC$^{-1}$

    AI explanation

    1. Analyze the question

    We are asked to find the electric field intensity ($E$) given the force ($F$) exerted on a charge and the magnitude of the charge ($q$).

    • Force ($F$) = 8 N
    • Charge ($q$) = 4 μC (microcoulombs)

    2. Explain the concept

    The electric field intensity ($E$) at any point in an electric field is defined as the force per unit charge placed at that point. The formula is:

    $E = \frac{F}{q}$

    Important Note: Before calculating, you must convert the charge from microcoulombs (μC) to the standard SI unit, Coulombs (C).

    • $1 \mu C = 10^{-6} C$
    • Therefore, $4 \mu C = 4 \times 10^{-6} C$

    3. Show the solution

    • Step 1: List the given values. • $F = 8 \, \text{N}$ • $q = 4 \times 10^{-6} \, \text{C}$

    • Step 2: Substitute the values into the formula. $$E = \frac{8}{4 \times 10^{-6}}$$

    • Step 3: Perform the division. • Divide the numbers: $8 \div 4 = 2$ • Handle the power of ten: $\frac{1}{10^{-6}} = 10^6$

    • Step 4: Combine the results. $$E = 2 \times 10^6 \, \text{NC}^{-1}$$

    4. Identify the answer

    Comparing our result to the given options, the correct value is $2.0 \times 10^6 \, \text{NC}^{-1}$. This matches option A.

    5. Tip

    Always watch out for prefixes like micro ($\mu = 10^{-6}$), milli ($m = 10^{-3}$), or nano ($n = 10^{-9}$) in JAMB Physics questions. Forgetting to convert these to standard units is the most common reason students lose marks in electricity calculations!

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12. 12.

    Which of the following materials has a very large energy gap band?

    1. A.Conductor
    2. B.Insulator
    3. C.Semiconductor
    4. D.Intrinsic semiconductor

    Show answer

    Answer: B. Insulator

    AI explanation

    1. Analyze the question

    The question asks us to identify which type of material possesses a "very large energy gap" (also known as a forbidden energy gap) between its valence band and its conduction band.

    2. Explain the concept

    In solid-state physics, materials are classified based on their energy band structure:

    • Conductors: The valence band and the conduction band overlap. There is essentially no energy gap, which allows electrons to move freely, resulting in high electrical conductivity.
    • Semiconductors: There is a small energy gap (usually around 1 eV). At room temperature, some electrons gain enough thermal energy to jump across this gap into the conduction band, allowing for moderate conductivity.
    • Insulators: There is a very large energy gap (typically greater than 5 eV). Because this gap is so wide, electrons in the valence band cannot gain enough energy to jump into the conduction band under normal conditions. This makes insulators unable to conduct electricity.

    3. Show the solution

    • Conductors (Option A): No gap; electrons flow easily.
    • Insulators (Option B): Very large energy gap; electrons are "trapped" in the valence band, preventing conduction.
    • Semiconductors (Options C & D): Small energy gap; conductivity can be manipulated by temperature or doping.

    Since the question specifically asks for a material with a "very large energy gap," the insulator is the only material that fits this description.

    4. Identify the answer

    The correct option is B.

    5. Exam Tip

    Think of the energy gap as a "hurdle" for electrons.

    • Conductor: No hurdle (easy flow).
    • Semiconductor: A small hurdle (jumpable with a little effort/heat).
    • Insulator: A massive wall (impossible to jump).

    Remember: Insulators = Large Gap = No Current.

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13. 13.

    A hydrometer of mass y kg and volume 2y x 10$^{-5}$m$^3$ floats in a fluid with 20% of its volume above the fluid, what is the density of the fluid?

    1. A.6.22 x 10$^4$kgm$^{-3}$
    2. B.6.23 x 10$^4$kgm$^{-3}$
    3. C.6.24 x 10$^4$kgm$^{-3}$
    4. D.6.25 x 10$^4$kgm$^{-3}$

    Show answer

    Answer: D. 6.25 x 10$^4$kgm$^{-3}$

    AI explanation

    Analysis

    To solve this problem, we apply the Law of Flotation, which states that for an object floating in equilibrium, the weight of the object is equal to the weight of the fluid displaced (Archimedes' Principle).

    Concept

    • Weight of the hydrometer ($W$): $W = mg = y \times g$
    • Volume of fluid displaced ($V_{disp}$): Since 20% of the volume is above the fluid, 80% of the volume is submerged. • $V_{submerged} = 0.80 \times V_{total}$ • $V_{total} = 2y \times 10^{-5} \, \text{m}^3$ • $V_{submerged} = 0.80 \times (2y \times 10^{-5}) = 1.6y \times 10^{-5} \, \text{m}^3$
    • Weight of fluid displaced ($W_{fluid}$): $W_{fluid} = \text{mass of fluid} \times g = (\rho \times V_{submerged}) \times g$ • Where $\rho$ is the density of the fluid.

    Solution

    1. Set the weight of the object equal to the weight of the displaced fluid: $$y \times g = \rho \times V_{submerged} \times g$$

    2. Cancel $g$ from both sides: $$y = \rho \times V_{submerged}$$

    3. Substitute the known values: $$y = \rho \times (1.6y \times 10^{-5})$$

    4. Solve for $\rho$: $$\rho = \frac{y}{1.6y \times 10^{-5}}$$The$y$cancels out:$$\rho = \frac{1}{1.6 \times 10^{-5}}$$ $$\rho = \frac{1}{1.6} \times 10^5$$ $$\rho = 0.625 \times 10^5$$

    5. Convert to standard scientific notation: $$\rho = 6.25 \times 10^4 \, \text{kgm}^{-3}$$

    Conclusion

    Comparing our result to the given options, we find that the calculated density matches option D.

    Exam Tip

    When dealing with "floating" problems, always remember that the density of the object relative to the fluid is equal to the fraction of the object that is submerged. In this case, $\frac{\rho_{object}}{\rho_{fluid}} = 0.8$. You can use this ratio shortcut to save time in the exam hall!

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14. 14.

    The power of a convex lens of focal length 20cm is

    1. A.0.05D
    2. B.0.50D
    3. C.5.00D
    4. D.50.00D

    Show answer

    Answer: C. 5.00D

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

16. 16.

    5 X 10$^{-3}$kg of liquid at its boiling point is evaporated in 20s by the heat generated by a resistor of 2$\Omega$ when a current of 10A is used. The specific latent heat of vaporization of the liquid is

    1. A.8.0 x 10$^4$Jkg$^{-1}$
    2. B.8.0 x 10$^5$Jkg$^{-1}$
    3. C.8.0 x 10$^6$Jkg$^{-1}$
    4. D.8.0 x 10$^7$Jkg$^{-1}$

    Show answer

    Answer: B. 8.0 x 10$^5$Jkg$^{-1}$

    AI explanation

    Analysis

    To solve this problem, we need to equate the electrical energy supplied by the resistor to the heat energy required to vaporize the liquid.

    Concept

    1. Electrical Energy ($H$): The heat generated by an electric current flowing through a resistor is given by Joule's Law: $H = I^2Rt$ Where: • $I$ = Current (in Amperes) • $R$ = Resistance (in Ohms) • $t$ = Time (in seconds)

    2. Heat of Vaporization ($Q$): The heat energy required to change a substance from liquid to gas at its boiling point is: $Q = mL_v$ Where: • $m$ = Mass (in kg) • $L_v$ = Specific latent heat of vaporization (in Jkg$^{-1}$)

    Since the electrical energy is used to evaporate the liquid, we set $H = Q$.

    Step-by-Step Solution

    Step 1: Calculate the electrical energy ($H$) Given:

    • $I = 10\text{ A}$
    • $R = 2\text{ }\Omega$
    • $t = 20\text{ s}$

    $H = I^2Rt$ $H = (10)^2 \times 2 \times 20$ $H = 100 \times 2 \times 20$ $H = 4000\text{ J}$

    Step 2: Calculate the specific latent heat ($L_v$) Given:

    • $m = 5 \times 10^{-3}\text{ kg}$
    • $H = 4000\text{ J}$

    Using $H = mL_v$: $4000 = (5 \times 10^{-3}) \times L_v$

    $L_v = \frac{4000}{5 \times 10^{-3}}$ $L_v = \frac{4000}{0.005}$ $L_v = 800,000\text{ Jkg}^{-1}$

    Step 3: Convert to standard form $800,000 = 8.0 \times 10^5\text{ Jkg}^{-1}$

    Conclusion

    Comparing our result with the given options, we find that the calculated value matches option B.

    Exam Tip: Always check your units before calculating! In JAMB Physics, mass is almost always expected in kilograms (kg). If the question had given the mass in grams, you would have needed to divide by 1000 first to avoid a common pitfall.

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17. 17.

    The gravitational force between two objects  masses 10$^{24}$kg and 10$^{27}$kg is 6.67N. Calculate the distance between them [ G = 6.6 x 10$^{-11}$Nm$^2$kg$^{-2}$ ]

    1. A.1.0 x 10$^{20}$m
    2. B.2.0 x 10$^{-20}$m
    3. C.1.0 x 10$^{-20}$m
    4. D.2.0 x 10$^{20}$m

    Show answer

    Answer: A. 1.0 x 10$^{20}$m

    AI explanation

    Analysis

    To solve this problem, we use Newton’s Law of Universal Gravitation, which states that the force ($F$) between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

    Concept

    The formula is:

    $F = \frac{G \cdot m_1 \cdot m_2}{r^2}$

    Where:

    • $F$ = Gravitational force ($6.67 \, \text{N}$)
    • $G$ = Gravitational constant ($6.67 \times 10^{-11} \, \text{Nm}^2\text{kg}^{-2}$)
    • $m_1$ = Mass 1 ($10^{24} \, \text{kg}$)
    • $m_2$ = Mass 2 ($10^{27} \, \text{kg}$)
    • $r$ = Distance between the objects (what we need to find)

    Step-by-Step Solution

    1. Rearrange the formula to solve for $r$: $$r^2 = \frac{G \cdot m_1 \cdot m_2}{F}$$

    2. Substitute the given values into the equation: $$r^2 = \frac{(6.67 \times 10^{-11}) \times (10^{24}) \times (10^{27})}{6.67}$$

    3. Simplify the calculation: • The $6.67$ in the numerator and denominator cancel each other out: $$r^2 = 10^{-11} \times 10^{24} \times 10^{27}$$ • Use the law of indices ($a^m \times a^n = a^{m+n}$): $$r^2 = 10^{(-11 + 24 + 27)}$$ $$r^2 = 10^{40}$$

    4. Find the square root to get $r$: $$r = \sqrt{10^{40}}$$ $$r = 10^{20} \, \text{m}$$

    This can be written as $1.0 \times 10^{20} \, \text{m}$.

    Conclusion

    Comparing our result to the given options, we find that it matches option A.

    Exam Tip: When dealing with powers of 10 in physics calculations, always handle the coefficients (the numbers in front) separately from the exponents. This prevents errors when moving decimals. Also, remember that $\sqrt{10^{40}}$ is simply $10^{40/2} = 10^{20}$.

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18. 18.

    The velocity ratio of an inclined plane at 60º to the horizontal is

    1. A.1.055
    2. B.1.155
    3. C.1.255
    4. D.2.00

    Show answer

    Answer: B. 1.155

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19. 19.

    A cell of internal resistance of 2$\Omega$ supplies current through a resistor, X if the efficiency of the cell is 75%, find the value of X.

    1. A.2$\Omega$
    2. B.4$\Omega$
    3. C.6$\Omega$
    4. D.8$\Omega$

    Show answer

    Answer: C. 6$\Omega$

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20. 20.

    The quantity of heat required to melt ice of 0.2 kg whose specific latent heat is 3.4 x 10$^5$J/Kg is

    1. A.6.8 x 10$^4$J
    2. B.8.6 x 10$^4$J
    3. C.1.7 x 10$^5$J
    4. D.1.7 x 10$^6$J

    Show answer

    Answer: A. 6.8 x 10$^4$J

    AI explanation

    Analysis

    To solve this problem, we need to calculate the amount of heat energy required to change the state of a substance (ice to water) without changing its temperature. This is a classic application of the principle of latent heat.

    Concept

    The quantity of heat ($Q$) required to change the state of a substance is given by the formula:

    $Q = mL$

    Where:

    • $Q$ = Quantity of heat (measured in Joules, J)
    • $m$ = Mass of the substance (measured in kilograms, kg)
    • $L$ = Specific latent heat of fusion (measured in J/kg)

    Solution

    Step 1: Identify the given values

    • Mass ($m$) = $0.2 \text{ kg}$
    • Specific latent heat ($L$) = $3.4 \times 10^5 \text{ J/kg}$

    Step 2: Substitute the values into the formula

    $Q = 0.2 \times (3.4 \times 10^5)$

    Step 3: Perform the calculation

    $Q = 0.2 \times 340,000$

    $Q = 68,000 \text{ J}$

    Step 4: Express in standard form To match the format of the options, we convert $68,000$ to standard form:

    $68,000 = 6.8 \times 10^4 \text{ J}$

    Conclusion

    Comparing our result to the provided options, $6.8 \times 10^4 \text{ J}$ corresponds to option A.

    Exam Tip

    When dealing with latent heat questions, always check the units. If the mass is given in grams, you must convert it to kilograms (divide by 1000) before multiplying by the specific latent heat, as the standard unit for $L$ is J/kg. Also, remember that "latent" means "hidden"—the temperature doesn't rise during this process, it only changes state!

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21. 21.

    A light ray passing from air into water at an angle of 30º from the normal in air would

    1. A.make an angle greater than 30$^0$ in water surface
    2. B.be completely absorbed by the water surface
    3. C.be completely reflected by the water surface
    4. D.make an angle less than 30$^0$ from the normal in water

    Show answer

    Answer: D. make an angle less than 30$^0$ from the normal in water

    AI explanation

    1. Analyze the question

    We are looking at the behavior of a light ray as it travels from a less dense medium (air) into a denser medium (water). We need to determine how the angle of refraction compares to the angle of incidence ($30^\circ$).

    2. Explain the concept

    This problem is governed by Snell's Law of Refraction, which states:

    $n_1 \sin(i) = n_2 \sin(r)$

    Where:

    • $n_1$ is the refractive index of the first medium (air $\approx 1.0$)
    • $n_2$ is the refractive index of the second medium (water $\approx 1.33$)
    • $i$ is the angle of incidence ($30^\circ$)
    • $r$ is the angle of refraction

    The Principle: When light travels from an optically less dense medium (like air) to an optically denser medium (like water), the light ray bends towards the normal. This means the angle of refraction ($r$) will be smaller than the angle of incidence ($i$).

    3. Show the solution

    • Step 1: Identify the refractive indices. Air has a refractive index of approximately 1.0, while water has a refractive index of approximately 1.33.
    • Step 2: Apply the rule of refraction. Since $n_{water} > n_{air}$, the light ray must bend towards the normal.
    • Step 3: Compare the angles. Because the ray bends towards the normal, the angle it makes with the normal in the water ($r$) must be smaller than the angle it made with the normal in the air ($i$).
    • Step 4: Calculation (conceptual): $$\sin(r) = \frac{n_1 \sin(i)}{n_2} = \frac{1.0 \times \sin(30^\circ)}{1.33}$$Since$\sin(30^\circ) = 0.5$, then$\sin(r) = \frac{0.5}{1.33} \approx 0.376$. Since$\sin(r) < \sin(30^\circ)$, it follows that$r < 30^\circ$.

    4. Identify the answer

    The angle of refraction is less than the angle of incidence because the light is moving into a denser medium. This matches option D.

    5. Tip

    Use the mnemonic "DENT": Denser to Entry (or air), Normal Turns away. Conversely, when going from Air to Water (Less to Denser), the light bends towards the normal, making the angle smaller.

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22. 22.

    The energy of light of frequency 2.0 x 10$^{15}$Hz is  (h = 6.63 x 10$^{-34}$Js)

    1. A.3.33 x 10$^{-18}$J
    2. B.1.33 x 10$^{-18}$J
    3. C.1.33 x 10$^{-19}$J
    4. D.3.33 x 10$^{-19}$J

    Show answer

    Answer: B. 1.33 x 10$^{-18}$J

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23. 23.

    A particular household utilizes three electrical appliances for six hours daily if the appliances are rated 80W, 100W, and 120W respectively. Calculate the electrical bills paid monthly if an average month is 31 days. [1kwh = #24.08k]

    1. A.₦ 2843.22k
    2. B.₦ 1950.22k
    3. C.₦ 1343.66k
    4. D.₦ 46.23k

    Show answer

    Answer: C. ₦ 1343.66k

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24. 24.

    The mechanical advantage of the machine shown above

    1. A.7.5
    2. B.15.5
    3. C.30.0
    4. D.60.0

    Show answer

    Answer: C. 30.0

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25. 25.

    If the velocity ratio of a machine is 4, what does it mean?

    1. A.Load and the effort are equal.
    2. B.Distance moved by effort is 4 times greater than the distance moved by load.
    3. C.The efficiency is low
    4. D.The load is greater than the effort

    Show answer

    Answer: B. Distance moved by effort is 4 times greater than the distance moved by load.

    AI explanation

    1. Analyze the question

    The question asks for the physical interpretation of a Velocity Ratio (V.R.) of 4 in a simple machine.

    2. Explain the concept

    In Physics, the Velocity Ratio (V.R.) of a machine is defined as the ratio of the distance moved by the effort ($d_e$) to the distance moved by the load ($d_l$) in the same time interval.

    The formula is:

    $V.R. = \frac{\text{Distance moved by effort}}{\text{Distance moved by load}} = \frac{d_e}{d_l}$

    When a machine has a V.R. of 4, it means that for every unit of distance the load moves, the effort must move 4 times that distance. This is a fundamental principle of machines: what you lose in distance (by moving the effort further), you gain in force (mechanical advantage).

    3. Show the solution

    • Given: $V.R. = 4$
    • Using the formula: $4 = \frac{d_e}{d_l}$
    • Rearranging the equation: $d_e = 4 \times d_l$

    This confirms that the distance moved by the effort ($d_e$) is 4 times the distance moved by the load ($d_l$).

    • Option A is incorrect because if the load and effort were equal, the Mechanical Advantage would be 1, not necessarily related to the V.R.
    • Option C is incorrect because V.R. does not determine efficiency; efficiency depends on the relationship between Mechanical Advantage and V.R.
    • Option D is incorrect because the load being greater than the effort refers to the Mechanical Advantage, not the Velocity Ratio.

    4. Identify the answer

    The correct interpretation is that the effort travels four times the distance that the load travels. This matches Option B.

    5. Tip

    Remember the mnemonic "V.E.L.": Velocity ratio = Effort distance / Load distance. Always keep in mind that V.R. is purely a measure of distance, while Mechanical Advantage (M.A.) is a measure of force.

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26. 26.

    Rainbow is formed when sunlight undergoes

    1. A.reflection
    2. B.refraction
    3. C.dispersion
    4. D.diffraction

    Show answer

    Answer: C. dispersion

    AI explanation

    1. Analyze the Question

    The question asks for the specific optical phenomenon responsible for the formation of a rainbow when sunlight interacts with water droplets in the atmosphere.

    2. Explain the Concept

    A rainbow is a meteorological phenomenon caused by the interaction of sunlight with raindrops. This process involves three main stages:

    • Refraction: As sunlight enters a raindrop, it slows down and bends.
    • Dispersion: Because white light is composed of different colors (wavelengths), each color bends at a slightly different angle. This separates the white light into its constituent colors (the visible spectrum: Red, Orange, Yellow, Green, Blue, Indigo, Violet).
    • Internal Reflection: The light hits the back of the raindrop and reflects off it, then exits the drop, undergoing further refraction.

    While reflection and refraction are involved, the primary phenomenon that causes the separation of white light into the distinct colors of the rainbow is dispersion.

    3. Show the Solution

    • Step 1: Sunlight (white light) enters a spherical water droplet.
    • Step 2: The light undergoes refraction at the surface of the droplet.
    • Step 3: The light is split into its component colors because different wavelengths travel at different speeds in the water. This splitting of white light into its spectrum is the definition of dispersion.
    • Step 4: The light reflects off the back of the droplet and exits, reaching our eyes as a spectrum of colors.

    Among the options provided, dispersion is the most accurate description of the phenomenon that creates the color spectrum we see as a rainbow.

    4. Identify the Answer

    The correct option is C.

    5. Exam Tip

    Remember the acronym ROYGBIV for the colors of the rainbow. When you see "rainbow" and "colors" in a physics question, your mind should immediately go to dispersion. If the question asks for the cause of the color separation, it is dispersion; if it asks for the bending of light, it is refraction.

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27. 27.

    The acceleration of a free fall due to gravity is not a constant everywhere on the Earth's surface because

    1. A.mass of the earth
    2. B.elliptical shape of the earth
    3. C.variation in the density of the earth
    4. D.rotation of the earth about its axis

    Show answer

    Answer: B. elliptical shape of the earth

    AI explanation

    Analysis

    The question asks why the acceleration due to gravity ($g$) varies across different points on the Earth's surface. We know that $g$ is defined by the formula:

    $g = \frac{GM}{R^2}$

    Where:

    • $G$ is the universal gravitational constant.
    • $M$ is the mass of the Earth.
    • $R$ is the distance from the center of the Earth to the point on the surface.

    Concept Explanation

    The value of $g$ depends primarily on the distance ($R$) from the Earth's center. If the Earth were a perfect sphere, $R$ would be constant everywhere, and $g$ would be the same. However, the Earth is not a perfect sphere; it is an oblate spheroid. It bulges at the equator and is flattened at the poles.

    Because of this shape:

    1. At the poles: The surface is closer to the center of the Earth (smaller $R$). Since $g$ is inversely proportional to $R^2$, a smaller $R$ results in a higher value of $g$.
    2. At the equator: The surface is further from the center of the Earth (larger $R$). A larger $R$ results in a lower value of $g$.

    Step-by-Step Solution

    1. Identify the variables: In the formula $g = \frac{GM}{R^2}$, $G$ and $M$ are constant for the Earth.
    2. Analyze the geometry: The Earth's radius is not uniform. The equatorial radius is larger than the polar radius due to the Earth's rotation during its formation.
    3. Apply the relationship: Since $g \propto \frac{1}{R^2}$, the variation in the radius ($R$) directly causes the variation in the acceleration due to gravity ($g$).
    4. Evaluate the options: While the rotation of the Earth (Option D) does contribute to the apparent gravity, the primary physical reason for the variation in the gravitational field itself across the surface is the Earth's non-spherical (elliptical) shape.

    Conclusion

    The elliptical shape (oblate spheroid) means the distance from the Earth's center varies with latitude, leading to the observed differences in $g$.

    Exam Tip

    Remember the "Pole-Equator" rule: Gravity is strongest at the poles (where you are closer to the center) and weakest at the equator (where you are further away). If you ever forget this, just remember that the Earth is "squashed" at the poles, making you closer to the core!

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28. 28.

    How much joules of heat are given out when a piece of iron, of mass 60g and specific heat capacity 460JKg$^{-1}$K$^{-1}$, cools from 75ºC to 35ºC

    1. A.1000J
    2. B.1050J
    3. C.1067J
    4. D.1104J

    Show answer

    Answer: D. 1104J

    AI explanation

    1. Analyze the Question

    We are asked to calculate the quantity of heat energy released ($Q$) by a piece of iron as it cools down. We are given:

    • Mass ($m$) = 60g
    • Specific heat capacity ($c$) = 460 J kg⁻¹ K⁻¹
    • Initial temperature ($T_1$) = 75ºC
    • Final temperature ($T_2$) = 35ºC

    2. Explain the Concept

    The amount of heat energy lost or gained by a substance is calculated using the formula:

    $Q = mc\Delta\theta$

    Where:

    • $m$ is the mass in kilograms (kg).
    • $c$ is the specific heat capacity.
    • $\Delta\theta$ is the change in temperature ($T_1 - T_2$).

    Important Note: Always ensure the mass is in kilograms (SI unit) to match the specific heat capacity unit (J kg⁻¹ K⁻¹).

    3. Show the Solution

    Step 1: Convert mass to kilograms

    $m = 60\text{g} = \frac{60}{1000}\text{kg} = 0.06\text{kg}$

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

    $\Delta\theta = 75^\circ\text{C} - 35^\circ\text{C} = 40^\circ\text{C} \text{ (or } 40\text{K)}$

    Step 3: Calculate the heat energy ($Q$)

    $Q = 0.06 \times 460 \times 40$

    $Q = 0.06 \times 18400$

    $Q = 1104\text{J}$

    4. Identify the Answer

    Comparing our result to the given options, the calculated value is 1104J, which corresponds to option D.

    5. Exam Tip

    In physics calculations, unit consistency is key. Many students lose marks because they forget to convert grams to kilograms. Always check if your mass is in grams; if it is, divide by 1000 immediately before plugging it into your formula!

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29. 29.

    Two points on a velocity-time graph have coordinates (2s, 5m/s) and (4s, 15m/s). Calculate the mean acceleration

    1. A.5.0ms$^2$
    2. B.0.83ms$^2$
    3. C.1.5ms$^2$
    4. D.2.0ms$^2$

    Show answer

    Answer: A. 5.0ms$^2$

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30. 30.

    At a pressure of 10$^5$Nm$^{-2}$, a gas has a volume of 20m$^3$. Calculate the volume at 4 x 10$^5$Nm$^{-2}$ at constant temperature.

    1. A.2m$^3$
    2. B.3m$^3$
    3. C.4m$^3$
    4. D.5m$^3$

    Show answer

    Answer: D. 5m$^3$

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31. 31.

    If a sheet of an insulating material is inserted between the plates of an air capacitor, the capacitance will

    1. A.become zero
    2. B.decrease
    3. C.increase
    4. D.remain unchanged

    Show answer

    Answer: C. increase

    AI explanation

    Analysis

    The question asks how the capacitance of an air-filled capacitor changes when an insulating material (a dielectric) is placed between its plates.

    Concept Explanation

    The capacitance ($C$) of a parallel-plate capacitor is given by the formula:

    $C = \frac{\varepsilon_0 A}{d}$

    Where:

    • $\varepsilon_0$ is the permittivity of free space (air).
    • $A$ is the area of the plates.
    • $d$ is the distance between the plates.

    When you insert an insulating material (a dielectric) with a dielectric constant ($\varepsilon_r$) greater than 1, the formula becomes:

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

    Since the dielectric constant ($\varepsilon_r$) of any insulating material is always greater than that of air (which is approximately 1), multiplying the original capacitance by $\varepsilon_r$ will result in a larger value.

    Step-by-Step Solution

    1. Identify the initial state: The capacitor is filled with air, so its capacitance is $C_{air} = \frac{\varepsilon_0 A}{d}$.
    2. Introduce the dielectric: When an insulator is inserted, the permittivity of the medium between the plates changes from $\varepsilon_0$ to $\varepsilon = \varepsilon_r \varepsilon_0$.
    3. Calculate the new capacitance: The new capacitance $C_{new} = \frac{\varepsilon_r \varepsilon_0 A}{d}$.
    4. Compare: Since $\varepsilon_r > 1$, it follows that $C_{new} > C_{air}$. Therefore, the capacitance increases.

    Conclusion

    Inserting a dielectric material reduces the electric field strength between the plates for a given charge, which allows the capacitor to store more charge at the same potential difference. Thus, the capacitance increases.

    Exam Tip: Always remember the mnemonic "D-I-I": Dielectric Insertion Increases capacitance. This will help you quickly recall the relationship in the exam hall!

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32. 32.

    The force of attraction between molecules of the same substance is

    1. A.cohesion
    2. B.capillarity
    3. C.adhesion
    4. D.surface tension

    Show answer

    Answer: A. cohesion

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

34. 34.

    The fourth overtone of a closed pipes is 900Hz, its fundamental frequency is

    1. A.50Hz
    2. B.100Hz
    3. C.200Hz
    4. D.400Hz

    Show answer

    Answer: B. 100Hz

    AI explanation

    1. Analyze the question

    We are given the frequency of the fourth overtone of a closed pipe (900 Hz) and asked to find the fundamental frequency ($f_0$).

    2. Explain the concept

    In a closed pipe (a pipe closed at one end and open at the other), the air column vibrates in odd harmonics only. The relationship for the frequencies of a closed pipe is given by:

    $f_n = (2n + 1)f_0$

    Where:

    • $f_n$ is the frequency of the $n^{th}$ overtone.
    • $n$ is the overtone number ($n = 0, 1, 2, 3, \dots$).
    • $f_0$ is the fundamental frequency.

    For a closed pipe:

    • Fundamental frequency ($f_0$) = $1f_0$
    • First overtone = $3f_0$
    • Second overtone = $5f_0$
    • Third overtone = $7f_0$
    • Fourth overtone = $9f_0$

    3. Show the solution

    • Step 1: Identify the formula for the fourth overtone. Based on the sequence above, the $n^{th}$ overtone of a closed pipe is $(2n + 1)f_0$. For the 4th overtone ($n=4$): $$f_4 = (2(4) + 1)f_0 = 9f_0$$

    • Step 2: Substitute the given value into the equation. We are told the fourth overtone is 900 Hz: $$900 = 9f_0$$

    • Step 3: Solve for $f_0$. $$f_0 = \frac{900}{9}$$ $$f_0 = 100 \text{ Hz}$$

    4. Identify the answer

    The fundamental frequency is 100 Hz. This corresponds to option B.

    5. Tip

    Memory Trick: For closed pipes, remember the sequence of multipliers is always odd numbers: 1, 3, 5, 7, 9...

    • Fundamental = 1st harmonic (1)
    • 1st overtone = 3rd harmonic (3)
    • 2nd overtone = 5th harmonic (5)
    • ...and so on. Just add 1 to the overtone number, multiply by 2, and subtract 1 to get the harmonic number! Or simply remember: Overtone $n$ = Harmonic $(2n+1)$.

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35. 35.

    The land and sea breeze is attributed to

    1. A.conduction and radiation
    2. B.conduction
    3. C.radiation
    4. D.convection

    Show answer

    Answer: D. convection

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36. 36.

    The property by which a material returns to its original shape after the removal of force is called

    1. A.Elasticity
    2. B.Ductility
    3. C.Malleability
    4. D.Plasticity

    Show answer

    Answer: A. Elasticity

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37. 37.

    The energy in a moving car is an example of

    1. A.Mechanical energy
    2. B.Electrical energy
    3. C.Potential energy
    4. D.Kinetic energy

    Show answer

    Answer: D. Kinetic energy

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38. 38.

    An electron falls from an energy level of -5.44eV to another energy level, E. If the emitted photon is of wavelength 5.68 x 10$^{-6}$m, calculate the energy change. [ Plank's constant = 6.63 x 10$^{-34}$Js, emitted radiation speed = 3.0 x 10$^8$ms$^{-1}$]

    1. A.1.49 x 10$^{-20}$J
    2. B.1.49 x 10$^{-19}$J
    3. C.3.49 x 10$^{-20}$J
    4. D.3.49 x 10$^{-19}$J

    Show answer

    Answer: C. 3.49 x 10$^{-20}$J

    AI explanation

    1. Analyze the Question

    We are given an electron transitioning between two energy levels. We need to find the energy change ($\Delta E$) of the emitted photon, given its wavelength ($\lambda$), Planck’s constant ($h$), and the speed of light ($c$).

    2. Explain the Concept

    When an electron moves from a higher energy level to a lower one, it emits a photon. The energy of this photon is exactly equal to the difference in energy between the two levels. The relationship between energy and wavelength is given by the formula:

    $E = \frac{hc}{\lambda}$

    Where:

    • $E$ = Energy in Joules (J)
    • $h$ = Planck’s constant ($6.63 \times 10^{-34} \text{ Js}$)
    • $c$ = Speed of light ($3.0 \times 10^8 \text{ ms}^{-1}$)
    • $\lambda$ = Wavelength ($5.68 \times 10^{-6} \text{ m}$)

    3. Show the Solution

    Step 1: Plug the values into the formula.

    $E = \frac{(6.63 \times 10^{-34}) \times (3.0 \times 10^8)}{5.68 \times 10^{-6}}$

    Step 2: Multiply the numerator.

    $(6.63 \times 3.0) \times 10^{-34 + 8} = 19.89 \times 10^{-26}$

    Step 3: Divide by the wavelength.

    $E = \frac{19.89 \times 10^{-26}}{5.68 \times 10^{-6}}$

    $E = \left(\frac{19.89}{5.68}\right) \times 10^{-26 - (-6)}$

    $E \approx 3.5017 \times 10^{-20} \text{ J}$

    Comparing this result to the provided options, $3.50 \times 10^{-20} \text{ J}$ is closest to $3.49 \times 10^{-20} \text{ J}$.

    4. Identify the Answer

    The calculated energy change is approximately $3.49 \times 10^{-20} \text{ J}$. This matches option C.

    5. Exam Tip

    When solving physics problems involving very small or large numbers, always handle the powers of 10 separately from the coefficients. This prevents calculation errors. Also, remember that $1 \text{ eV} = 1.6 \times 10^{-19} \text{ J}$; if the question had asked for the answer in electron-volts, you would divide your final answer by $1.6 \times 10^{-19}$.

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39. 39.

    A load of 300N is to be lifted by a machine with a velocity ratio of 2 and an efficiency of 60%. What effort will be applied to lift the load?

    1. A.100N
    2. B.150N
    3. C.250N
    4. D.400N

    Show answer

    Answer: C. 250N

    AI explanation

    Analysis

    To solve this problem, we need to understand the relationship between Efficiency ($\eta$), Mechanical Advantage (MA), and Velocity Ratio (VR).

    Concept

    1. Efficiency ($\eta$): This is the ratio of the work output to the work input, expressed as a percentage. The formula is: $$\eta = \frac{\text{Mechanical Advantage (MA)}}{\text{Velocity Ratio (VR)}} \times 100\%$$
    2. Mechanical Advantage (MA): This is the ratio of the Load ($L$) to the Effort ($E$): $$\text{MA} = \frac{\text{Load}}{\text{Effort}}$$

    Step-by-Step Solution

    Step 1: Identify the given values

    • Load ($L$) = $300\text{ N}$
    • Velocity Ratio (VR) = $2$
    • Efficiency ($\eta$) = $60\%$ (or $0.6$ in decimal form)

    Step 2: Calculate the Mechanical Advantage (MA) Using the efficiency formula:

    $0.6 = \frac{\text{MA}}{2}$

    $\text{MA} = 0.6 \times 2$

    $\text{MA} = 1.2$

    Step 3: Calculate the Effort ($E$) Now, use the MA formula to find the effort:

    $\text{MA} = \frac{\text{Load}}{\text{Effort}}$

    $1.2 = \frac{300}{E}$

    $E = \frac{300}{1.2}$

    $E = 250\text{ N}$

    Conclusion

    By applying the efficiency formula to find the mechanical advantage and then relating it to the load, we determine that an effort of $250\text{ N}$ is required.

    Exam Tip

    Always remember the relationship $\text{Efficiency} = \frac{\text{MA}}{\text{VR}}$. If you are ever confused, just remember that in a perfect machine (100% efficiency), the MA equals the VR. Since real machines are never 100% efficient, the MA will always be less than the VR.

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40. 40.

    The bursting of water pipes during very cold weather, when the water in the pipes form ice could be attributed to

    1. A.contraction of pipes when cooled
    2. B.expansion of water on freezing
    3. C.contraction of water on freezing
    4. D.expansion of ice on melting

    Show answer

    Answer: B. expansion of water on freezing

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41. 41.

    In electrolysis, when same quantity of electricity is passed through different electrolytes, mass of substances deposited is proportional to

    1. A.Molecular weight
    2. B.Chemical equivalent
    3. C.Atomic number
    4. D.Chemical equivalent per valency

    Show answer

    Answer: B. Chemical equivalent

    AI explanation

    Analysis

    The question asks for the relationship between the mass of substances deposited during electrolysis when the same quantity of electricity is passed through different electrolytes. This is a fundamental principle of Faraday's Laws of Electrolysis.

    Concept: Faraday’s Second Law of Electrolysis

    Faraday’s Second Law of Electrolysis states that when the same quantity of electricity is passed through different electrolytes connected in series, the masses of the substances deposited (or liberated) at the electrodes are directly proportional to their chemical equivalents (also known as equivalent weights).

    The chemical equivalent is calculated as:

    $\text{Chemical Equivalent} = \frac{\text{Molar Mass}}{\text{Valency (or oxidation state)}}$

    Step-by-Step Solution

    1. Understand the Law: Faraday's second law specifically addresses the comparison between different substances. It establishes that the amount of chemical change produced by a given quantity of electricity is proportional to the equivalent weight of the substance.
    2. Evaluate the Options: • A (Molecular weight): This is incorrect because it does not account for the valency of the ions. • B (Chemical equivalent): This matches the definition of Faraday's Second Law perfectly. • C (Atomic number): This is irrelevant to the mass deposited in electrolysis. • D (Chemical equivalent per valency): This is redundant and incorrect, as the chemical equivalent already incorporates the valency.
    3. Conclusion: Since the mass deposited ($m$) is related to the quantity of electricity ($Q$) and the chemical equivalent ($E$) by the formula $m = \frac{Q \times E}{F}$ (where $F$ is Faraday's constant), it is clear that $m \propto E$.

    Correct Answer

    The correct option is B.

    Exam Tip

    To remember this easily, think of the "E" in Electrolysis and Equivalent weight. Faraday's Second Law deals with different substances, and the key factor that distinguishes them in this process is their Equivalent weight.

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42. 42.

    An effort of 40N is applied on a machine to lift a mass of 60kg. Determine the mechanical advantage of the machine [ g = 10ms$^2$ ]

    1. A.2400
    2. B.240
    3. C.150
    4. D.15

    Show answer

    Answer: D. 15

    AI explanation

    Analysis

    To solve this problem, we need to calculate the Mechanical Advantage (MA) of the machine. The mechanical advantage is defined as the ratio of the load (the force exerted by the machine) to the effort (the force applied to the machine).

    Concept

    The formula for Mechanical Advantage is:

    $\text{MA} = \frac{\text{Load}}{\text{Effort}}$

    • Effort: The force applied to the machine (given as 40 N).
    • Load: The weight of the object being lifted. Since weight is a force, we calculate it using the formula: $$\text{Load} = \text{mass} \times \text{acceleration due to gravity} (g)$$ $$\text{Load} = m \times g$$

    Step-by-Step Solution

    1. Identify the given values: • Effort ($E$) = 40 N • Mass ($m$) = 60 kg • Acceleration due to gravity ($g$) = 10 m/s²

    2. Calculate the Load: $$\text{Load} = 60\text{ kg} \times 10\text{ m/s}^2$$ $$\text{Load} = 600\text{ N}$$

    3. Calculate the Mechanical Advantage (MA): $$\text{MA} = \frac{\text{Load}}{\text{Effort}}$$ $$\text{MA} = \frac{600\text{ N}}{40\text{ N}}$$ $$\text{MA} = \frac{60}{4}$$ $$\text{MA} = 15$$

    Conclusion

    The mechanical advantage of the machine is 15. This matches option D.

    Exam Tip

    Always remember that Mechanical Advantage is a ratio of two forces, which means it has no unit. If you ever calculate an MA and end up with units like Newtons or Kilograms, double-check your work! Also, ensure your mass is converted to weight (Newtons) before dividing by the effort.

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43. 43.

    The friction due to air mass can be reduced by

    1. A.streaming
    2. B.lubricating
    3. C.propeller
    4. D.polishing

    Show answer

    Answer: A. streaming

    AI explanation

    1. Analyze the question

    The question asks for the method used to minimize air resistance (also known as air drag) acting on an object moving through the air.

    2. Explain the concept

    Air resistance is a form of fluid friction that acts on objects moving through the atmosphere. When an object moves, it pushes air molecules out of its way. If the object has a blunt or irregular shape, it creates turbulence and high-pressure zones that slow it down.

    To reduce this, engineers use a process called streamlining. Streamlining involves designing an object with a smooth, tapered shape (like a teardrop or the body of an airplane) that allows air to flow smoothly around it, minimizing turbulence and drag.

    • Lubricating is used to reduce friction between two solid surfaces (like in a car engine).
    • Propellers are used to provide thrust or propulsion, not to reduce air resistance.
    • Polishing reduces surface roughness, which helps slightly, but it is not the primary engineering method for reducing air resistance compared to changing the shape of the object.

    3. Show the solution

    • Step 1: Identify the force involved. The question specifies "friction due to air mass," which is air resistance.
    • Step 2: Evaluate the options. • Lubricating: Used for solid-on-solid friction. Incorrect. • Propeller: Used for movement/thrust. Incorrect. • Polishing: Reduces surface friction, but does not address the aerodynamic drag caused by the shape of the object. • Streaming (Streamlining): This is the specific aerodynamic design principle used to allow air to flow past an object with minimal resistance.
    • Step 3: Conclusion. Streamlining is the standard scientific method for reducing air resistance.

    4. Identify the answer

    The correct option is A.

    5. Exam Tip

    Think of a fish or a bird. Their bodies are naturally "streamlined" to move through water and air with the least amount of resistance. Whenever you see a question about reducing air drag, always look for keywords like "streamlining," "tapered," or "aerodynamic shape."

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44. 44.

    Which of these gas laws is equivalent to workdone

    1. A.Charle's law
    2. B.Pressure law
    3. C.Boyle's law
    4. D.Gay Lussac's law

    Show answer

    Answer: C. Boyle's law

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45. 45.

    Infra-red thermometers work by detecting the

    1. A.radiation from the body and converting it to temperature
    2. B.conduction of heat from the body
    3. C.convective air pulse from the body
    4. D.absorption of heat by the body

    Show answer

    Answer: A. radiation from the body and converting it to temperature

    AI explanation

    1. Analyze the question

    The question asks for the physical principle behind the operation of an infra-red thermometer. We need to identify how these devices measure temperature without making physical contact with an object.

    2. Explain the concept

    All objects with a temperature above absolute zero emit electromagnetic radiation. This is known as thermal radiation or black-body radiation.

    • Infra-red (IR) thermometers are designed to detect the intensity of the infra-red radiation emitted by an object.
    • The device uses a lens to focus the infra-red energy onto a detector called a thermopile.
    • The thermopile absorbs the IR radiation and converts it into an electrical signal.
    • The device then uses an internal algorithm to convert that electrical signal into a temperature reading.

    Because this process relies on radiation, it does not require physical contact (unlike conduction) or the movement of air (unlike convection).

    3. Show the solution

    • Option A: Infra-red thermometers measure the thermal radiation emitted by an object. This is the correct physical principle.
    • Option B: Conduction requires physical contact between the thermometer and the object. IR thermometers are "non-contact" devices.
    • Option C: Convection involves the transfer of heat through the movement of fluids (like air). IR thermometers do not measure air pulses.
    • Option D: Absorption of heat by the body describes how an object gains heat, not how a thermometer measures the temperature of an object.

    4. Identify the answer

    The correct option is A.

    5. Exam Tip

    When you see "Infra-red" in a Physics question, immediately associate it with radiation. Remember that infra-red radiation is a form of electromagnetic wave that travels through a vacuum and does not require a medium to transfer heat. This is why you can measure the temperature of a hot object from a distance!

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46. 46.

    Calculate the depth of a swimming pool if the apparent depth is 10cm. ( Refractive index of water = 1.33 )

    1. A.7.5cm
    2. B.10.0cm
    3. C.13.3cm
    4. D.6.87cm

    Show answer

    Answer: C. 13.3cm

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47. 47.

    A boy standing 408m from a wall blew a trumpet and heard the echo 2.4s later. Calculate the speed of the sound

    1. A.310m/s
    2. B.320m/s
    3. C.330m/s
    4. D.340m/s

    Show answer

    Answer: D. 340m/s

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48. 48.

    The dimension of young's modulus,E is given by

    1. A.MLT$^{-1}$
    2. B.MT$^{-2}$
    3. C.ML$^{-1}$T$^{-2}$
    4. D.M$^{-1}$T

    Show answer

    Answer: C. ML$^{-1}$T$^{-2}$

    AI explanation

    To find the dimension of Young's Modulus ($E$), we need to look at its definition and the dimensions of the quantities involved.

    1. Analyze the Concept

    Young's Modulus ($E$) is defined as the ratio of Stress to Strain:

    $E = \frac{\text{Stress}}{\text{Strain}}$

    • Stress is defined as Force ($F$) per unit Area ($A$): $\text{Stress} = \frac{F}{A}$
    • Strain is defined as the change in length ($\Delta L$) divided by the original length ($L$): $\text{Strain} = \frac{\Delta L}{L}$

    2. Break Down the Dimensions

    • Force ($F$): From Newton's Second Law ($F = ma$), the dimension is $[M][L][T^{-2}]$.
    • Area ($A$): Area is length squared, so the dimension is $[L^2]$.
    • Stress: $\frac{[M][L][T^{-2}]}{[L^2]} = [M][L^{-1}][T^{-2}]$.
    • Strain: Since it is a ratio of two lengths ($\frac{L}{L}$), it is dimensionless. It has no units and no dimensions ($[M^0L^0T^0]$).

    3. Calculate the Dimension of Young's Modulus

    Since $E = \frac{\text{Stress}}{\text{Strain}}$, and Strain is dimensionless:

    $E = \text{Dimension of Stress}$

    $E = [M][L^{-1}][T^{-2}]$

    4. Conclusion

    Comparing our result $[ML^{-1}T^{-2}]$ to the given options:

    • A: $MLT^{-1}$
    • B: $MT^{-2}$
    • C: $ML^{-1}T^{-2}$
    • D: $M^{-1}T$

    The calculated dimension matches option C.

    Exam Tip

    Always remember that Stress, Pressure, and Young's Modulus all share the same dimension: $[ML^{-1}T^{-2}]$. If you ever forget the formula for Young's Modulus, just remember that it has the same units as Pressure (Newtons per square meter, $N/m^2$), which makes it easy to derive the dimensions from there!

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49. 49.

    Convert 60ºC to degree Fahrenheit

    1. A.111.15$^0$F
    2. B.115.56$^0$F
    3. C.132.23$^0$F
    4. D.140.00$^0$F

    Show answer

    Answer: D. 140.00$^0$F

    AI explanation

    Analysis

    To convert temperature from Celsius ($^\circ\text{C}$) to Fahrenheit ($^\circ\text{F}$), we use a standard linear conversion formula. This is a common topic in JAMB Physics under the "Heat Energy" module.

    Concept

    The relationship between the Celsius scale and the Fahrenheit scale is defined by the formula:

    $F = \left( \frac{9}{5} \times C \right) + 32$

    Where:

    • $F$ is the temperature in Fahrenheit.
    • $C$ is the temperature in Celsius.

    Solution

    Given that $C = 60^\circ\text{C}$, we substitute this value into the formula:

    1. Multiply by 9/5: $$\frac{9}{5} \times 60 = 9 \times 12 = 108$$ (Note: $60 \div 5 = 12$, and $12 \times 9 = 108$)

    2. Add 32: $$108 + 32 = 140$$

    So, $60^\circ\text{C} = 140^\circ\text{F}$.

    Conclusion

    Comparing our result to the given options, the correct value is 140.00$^\circ$F.

    Correct Option: D

    Exam Tip

    To remember the formula easily, think of the freezing and boiling points of water:

    • Water freezes at $0^\circ\text{C}$ ($32^\circ\text{F}$) and boils at $100^\circ\text{C}$ ($212^\circ\text{F}$).
    • The difference is $100$ degrees on the Celsius scale and $180$ degrees on the Fahrenheit scale ($212 - 32 = 180$).
    • The ratio $180/100$ simplifies to $9/5$. Always remember to add the $32$ offset because the scales don't start at the same point!

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50. 50.

    A rectifier is a device that changes

    1. A.D.C to D.C
    2. B.D.C to A.C
    3. C.A.C to A.C
    4. D.A.C to D.C

    Show answer

    Answer: D. A.C to D.C

    AI explanation

    1. Analyze the question

    The question asks for the primary function of a rectifier in an electrical circuit. You need to identify which type of current conversion it performs.

    2. Explain the concept

    In electronics, current comes in two main forms:

    • Alternating Current (A.C.): The flow of electric charge periodically reverses direction. This is the type of current supplied by the Power Holding Company of Nigeria (PHCN) to our homes.
    • Direct Current (D.C.): The flow of electric charge is in only one direction. This is the type of current required by most electronic devices (like your phone, laptop, or radio) to function.

    A rectifier is an electrical component (usually made of diodes) that allows current to flow in only one direction. By blocking the reverse flow of an A.C. signal, it effectively converts the oscillating A.C. into a unidirectional D.C. signal.

    3. Show the solution

    • Step 1: Understand that A.C. fluctuates between positive and negative values.
    • Step 2: A diode acts as a one-way valve. When placed in an A.C. circuit, it "chops off" the negative half of the cycle or flips it, ensuring the output current only moves in one direction.
    • Step 3: Since the output is now unidirectional, the process is defined as converting A.C. to D.C.

    4. Identify the answer

    Comparing our explanation to the options provided:

    • A is incorrect (D.C. to D.C. is handled by converters).
    • B is incorrect (D.C. to A.C. is performed by an inverter).
    • C is incorrect (A.C. to A.C. is typically handled by a transformer).
    • D is correct.

    C. to D.C.

    5. Exam Tip

    To remember this easily, use the mnemonic "R-A-D": Rectifier = A.C. to D.C. Conversely, remember that an Inverter does the opposite (D.C. to A.C.), which is why we use inverters at home to turn battery power (D.C.) into household power (A.C.) during a power outage.

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51. 51.

    If the pressure on an enclosed gas is doubled and its temperature rises from 27ºC to 127ºC, then its volume will

    1. A.increase by $\frac{2}{3^{rd}}$
    2. B.increase by $\frac{1}{3^{rd}}$
    3. C.decrease by $\frac{2}{3^{rd}}$
    4. D.decrease by $\frac{1}{3^{rd}}$

    Show answer

    Answer: D. decrease by $\frac{1}{3^{rd}}$

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52. 52.

    Find the amount of current required to deposit 0.02kg of metal in a given electrolysis for 120 seconds. [electro chemical equivalent of the metal = 1.3 x 10$^{-7}$kgC$^{-1}$]

    1. A.7.8 x 10$^{-4}$A
    2. B.7.8 x 10$^{-2}$A
    3. C.1.3 x 10$^3$A
    4. D.1.3 x 10$^5$A

    Show answer

    Answer: C. 1.3 x 10$^3$A

    AI explanation

    Analysis

    To solve this problem, we need to use Faraday’s First Law of Electrolysis, which relates the mass of a substance deposited during electrolysis to the quantity of electricity (charge) passed through the electrolyte.

    Concept

    Faraday's law states that the mass ($m$) of a substance deposited is given by the formula:

    $m = zIt$

    Where:

    • $m$ = mass of the metal deposited (in kg)
    • $z$ = electrochemical equivalent of the metal (in kg/C)
    • $I$ = current (in Amperes, A)
    • $t$ = time (in seconds, s)

    Solution

    Step 1: Identify the given values

    • Mass ($m$) = $0.02\text{ kg} = 2 \times 10^{-2}\text{ kg}$
    • Electrochemical equivalent ($z$) = $1.3 \times 10^{-7}\text{ kg/C}$
    • Time ($t$) = $120\text{ s}$

    Step 2: Rearrange the formula to solve for current ($I$)

    $I = \frac{m}{z \times t}$

    Step 3: Substitute the values into the equation

    $I = \frac{2 \times 10^{-2}}{(1.3 \times 10^{-7}) \times 120}$

    Step 4: Perform the calculation First, multiply the denominator:

    $1.3 \times 10^{-7} \times 120 = 156 \times 10^{-7} = 1.56 \times 10^{-5}$

    Now, divide the numerator by the denominator:

    $I = \frac{2 \times 10^{-2}}{1.56 \times 10^{-5}}$

    $I = \left(\frac{2}{1.56}\right) \times 10^{-2 - (-5)}$

    $I \approx 1.282 \times 10^3\text{ A}$

    Rounding to two significant figures as presented in the options, we get approximately $1.3 \times 10^3\text{ A}$.

    Conclusion

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

    Exam Tip

    When dealing with scientific notation in JAMB Physics, always convert your units to standard SI units first (e.g., grams to kilograms, minutes to seconds). Also, keep an eye on the powers of 10; a common mistake is miscalculating the exponent during division. Remember: when dividing, subtract the exponents ($10^a / 10^b = 10^{a-b}$).

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53. 53.

    Which of the following is not a part of model rocket?

    1. A.The body tube
    2. B.The nose cones
    3. C.The fin
    4. D.Not recovery devices

    Show answer

    Answer: D. Not recovery devices

    AI explanation

    Analysis of the Question

    This question tests your knowledge of the fundamental components of a model rocket. To answer this, we need to identify the standard parts that make up a functional model rocket and determine which option does not fit that description.

    Concept Explanation

    A model rocket is designed to be lightweight and aerodynamic. Its basic structure typically consists of:

    1. Body Tube: The main structural component that houses the engine, recovery system, and payload.
    2. Nose Cone: The front part of the rocket, shaped to reduce air resistance (drag) and improve stability.
    3. Fins: These are attached to the lower part of the body tube to provide stability during flight, ensuring the rocket flies straight.
    4. Recovery System: This is a crucial component (such as a parachute or streamer) that allows the rocket to return to the ground safely without being damaged.
    5. Engine Mount: The internal structure that holds the rocket motor in place.

    Step-by-Step Solution

    • Option A (The body tube): This is the primary structure of the rocket. It is definitely a part.
    • Option B (The nose cones): This is essential for aerodynamics and is a standard part of every model rocket.
    • Option C (The fin): Fins are necessary for flight stability. They are a standard part.
    • Option D (Not recovery devices): Recovery devices (like parachutes) are a standard part of a model rocket. Therefore, the statement "Not recovery devices" is incorrect because recovery devices are a part of the rocket. In the context of this multiple-choice question, this option is the "odd one out" because it denies the existence of a necessary component.

    Conclusion

    Since the body tube, nose cone, and fins are all essential parts, and recovery devices are also essential, Option D is the correct choice as it incorrectly identifies the status of recovery devices in relation to rocket construction.

    Exam Tip: When you see a question asking what is "not" a part of something, quickly list the standard components in your head. If you find a component listed in the options that is actually a part, look for the option that phrases its exclusion in a confusing or contradictory way.

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54. 54.

    As per Faraday's laws of electromagnetic induction, an e.m.f is induced in a conductor whenever

    1. A.lies parallel to the magnetic flux
    2. B.lies in a magnetic field
    3. C.lies out side but close to a magnetic field
    4. D.cuts magnetic flux

    Show answer

    Answer: D. cuts magnetic flux

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55. 55.

    The degree of precision of a vernier caliper is

    1. A.0.005cm
    2. B.0.01cm
    3. C.0.1cm
    4. D.1.0cm

    Show answer

    Answer: B. 0.01cm

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56. 56.

    The process of adding impurities to a semiconductor material to increase its conductivity is

    1. A.Rectification
    2. B.Emission
    3. C.Doping
    4. D.Stabilization

    Show answer

    Answer: C. Doping

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57. 57.

    At absolute zero temperature, the average velocity of the molecules

    1. A.Decreases
    2. B.Increases
    3. C.Is zero
    4. D.Is uncertain

    Show answer

    Answer: C. Is zero

    AI explanation

    1. Analyze the question

    The question asks for the behavior of the average velocity of gas molecules when the temperature of a system reaches absolute zero ($0\text{ K}$).

    2. Explain the concept

    In the Kinetic Theory of Gases, the temperature of a substance is a measure of the average kinetic energy of its molecules. The relationship is given by the formula:

    $K.E._{avg} = \frac{3}{2}kT$

    Where:

    • $K.E._{avg}$ is the average kinetic energy.
    • $k$ is the Boltzmann constant.
    • $T$ is the absolute temperature in Kelvin.

    Since kinetic energy is defined as $K.E. = \frac{1}{2}mv^2$, it follows that:

    $\frac{1}{2}mv^2 = \frac{3}{2}kT$

    $v^2 = \frac{3kT}{m}$

    From this equation, you can see that the velocity ($v$) is directly proportional to the square root of the absolute temperature ($\sqrt{T}$).

    3. Show the solution

    • Step 1: Identify the temperature at absolute zero. Absolute zero is $0\text{ K}$.
    • Step 2: Substitute $T = 0$ into the velocity relationship: $$v \propto \sqrt{0}$$ $$v = 0$$
    • Step 3: At $0\text{ K}$, the thermal motion of the particles ceases. Because there is no thermal energy to drive the movement of the molecules, their average velocity becomes zero.

    4. Identify the answer

    Based on the kinetic theory, at absolute zero, the molecules lose all their kinetic energy and come to a state of rest. Therefore, the average velocity is zero.

    The correct option is C.

    5. Exam Tip

    Always remember that in physics, "Absolute Zero" ($0\text{ K}$ or $-273.15^\circ\text{C}$) is the theoretical limit where all molecular motion stops. If you ever see a question about "absolute zero," think "zero energy" and "zero motion." This will help you quickly eliminate options that suggest the molecules are still moving or increasing in speed.

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58. 58.

    A wheelbarrow inclined at 60º to the horizontal is pushed with a force of 150N. What is the horizontal component of the applied force

    1. A.130N
    2. B.75N
    3. C.60N
    4. D.50N

    Show answer

    Answer: B. 75N

    AI explanation

    1. Analyze the question

    We are given a force ($F$) of 150N applied at an angle ($\theta$) of 60º to the horizontal. We need to find the horizontal component of this force.

    2. Explain the concept

    In physics, when a force is applied at an angle, it can be resolved into two perpendicular components:

    • Horizontal component ($F_x$): This is the part of the force acting along the x-axis (the ground). It is calculated using the cosine function: $$F_x = F \cos(\theta)$$
    • Vertical component ($F_y$): This is the part of the force acting along the y-axis (upwards). It is calculated using the sine function: $$F_y = F \sin(\theta)$$

    Since the question asks for the horizontal component, we will use the cosine formula.

    3. Show the solution

    • Given: • Force ($F$) = 150N • Angle ($\theta$) = 60º
    • Formula: • $F_x = F \cos(60º)$
    • Calculation: • We know that $\cos(60º) = 0.5$ (or $\frac{1}{2}$) • $F_x = 150 \times 0.5$ • $F_x = 75\text{N}$

    4. Identify the answer

    Comparing our result to the given options: A. 130N B. 75N C. 60N D. 50N

    The calculated value matches option B.

    5. Tip

    A simple way to remember which trig function to use: "Cos is close." The horizontal component is usually the one "closer" to the horizontal axis (the adjacent side of the triangle), so it always pairs with cosine. If you are ever confused, just remember CAH (Cosine = Adjacent / Hypotenuse).

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59. 59.

    The diaphragm in the camera is similar to what part of the eyes?

    1. A.Cornea
    2. B.Lens
    3. C.Ciliary muscle
    4. D.Iris

    Show answer

    Answer: D. Iris

    AI explanation

    Analysis

    The question asks us to identify the part of the human eye that performs a function analogous to the diaphragm of a camera.

    Concept Explanation

    To understand this, we must look at the function of both components:

    • Camera Diaphragm (Aperture): This is an adjustable opening that controls the amount of light entering the camera lens. By opening wider or closing tighter, it regulates the intensity of light reaching the film or sensor.
    • Human Eye: The eye also needs to regulate the amount of light entering it to protect the retina and ensure clear vision under different lighting conditions.

    Step-by-Step Solution

    1. Cornea (Option A): This is the transparent front part of the eye that acts as a fixed lens, helping to focus light. It does not control the amount of light.
    2. Lens (Option B): The eye lens changes shape to focus light onto the retina (accommodation). It is responsible for focusing, not for regulating light intensity.
    3. Ciliary muscle (Option C): These muscles control the shape of the eye lens to allow for focusing at different distances. They do not control light intensity.
    4. Iris (Option D): The iris is the colored part of the eye. It contains muscles that adjust the size of the pupil (the hole in the center). By changing the size of the pupil, the iris controls the amount of light that enters the eye, exactly like the diaphragm of a camera.

    Conclusion

    Since the iris regulates the light entering the eye by adjusting the pupil size, it is the direct equivalent of the camera's diaphragm.

    Exam Tip

    Think of it this way: "Iris = Intensity." Whenever you see a question about controlling the amount of light in the eye, always look for the Iris. If the question asks about focusing light, look for the Lens.

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60. 60.

    When a bus is accelerating, it must be

    1. A.changing its speed
    2. B.changing its velocity
    3. C.changing its position
    4. D.changing its direction

    Show answer

    Answer: B. changing its velocity

    AI explanation

    1. Analyze the question

    The question asks for the definition of acceleration in the context of a moving bus. We need to distinguish between speed, velocity, and position to identify what must happen for acceleration to occur.

    2. Explain the concept

    In physics, acceleration is defined as the rate of change of velocity with respect to time.

    It is crucial to understand the difference between speed and velocity:

    • Speed is a scalar quantity (it only has magnitude).
    • Velocity is a vector quantity (it has both magnitude and direction).

    Because velocity includes direction, an object is accelerating if:

    1. Its speed changes (speeding up or slowing down).
    2. Its direction changes (even if the speed remains constant, like a car turning a corner).
    3. Both its speed and direction change.

    3. Show the solution

    • Option A (changing its speed): While changing speed is a form of acceleration, it is not the only way to accelerate. An object moving at a constant speed in a circle is still accelerating because its direction is changing.
    • Option B (changing its velocity): Since velocity is defined as "speed in a given direction," any change in either speed or direction results in a change in velocity. Therefore, acceleration is defined as a change in velocity.
    • Option C (changing its position): An object can change its position (move) at a constant velocity (zero acceleration). Therefore, this is not the definition of acceleration.
    • Option D (changing its direction): Similar to Option A, this is only one specific type of acceleration.

    Since acceleration is mathematically defined as $a = \frac{\Delta v}{\Delta t}$ (where $v$ is velocity), the bus must be changing its velocity.

    4. Identify the answer

    The correct option is B.

    5. Tip

    Think of the "Velocity Vector": If you are driving a bus and you either press the gas pedal (change speed) or turn the steering wheel (change direction), you are changing your velocity. Both actions count as acceleration!

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

62. 62.

    The energy stored in the above capacitor is

    1. A.2.25J
    2. B.6.25J
    3. C.18.25J
    4. D.24.25J

    Show answer

    Answer: B. 6.25J

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63. 63.

    One of these is not the use of an electroscope

    1. A.testing the type of charge on a charge body
    2. B.measuring ionization current in air
    3. C.detecting the pressure of charge on a charged body
    4. D.producing electric charge in a body

    Show answer

    Answer: D. producing electric charge in a body

    AI explanation

    Analysis of the Question

    The question asks us to identify which of the listed functions is not a use of a gold-leaf electroscope. To answer this, we need to understand what an electroscope is designed to do in a physics laboratory.

    Concept Explanation

    A gold-leaf electroscope is a sensitive instrument used primarily for detecting and analyzing electric charges. Its main functions include:

    1. Detecting the presence of charge: It indicates whether an object is charged or neutral.
    2. Testing the type of charge: By charging the electroscope first, we can determine if an unknown body has a positive or negative charge based on whether the leaves diverge further or collapse.
    3. Comparing the magnitude of charges: The degree of divergence of the leaves gives an indication of the relative amount of charge.
    4. Testing conductivity: It helps determine if a material is a conductor or an insulator.
    5. Measuring ionization: It can be used to measure the ionization current in air, as ions in the air will cause a charged electroscope to discharge.

    Step-by-Step Evaluation

    • Option A (Testing the type of charge): This is a primary function of the electroscope. Correct.
    • Option B (Measuring ionization current in air): This is a known application of the electroscope in experimental physics. Correct.
    • Option C (Detecting the presence of charge): This is the most basic function of the electroscope. (Note: The question says "pressure of charge," which is a typographical error for "presence of charge"). Correct.
    • Option D (Producing electric charge in a body): An electroscope is a detection device, not a generator. It cannot create or produce electric charge. To produce charge, you would need methods like friction (triboelectric effect), induction, or conduction from an existing source.

    Conclusion

    Since the electroscope is strictly a measuring and detecting instrument, it cannot be used to generate or produce electric charges. Therefore, option D is the correct answer as it describes a function the electroscope cannot perform.

    Exam Tip: Whenever you see questions about laboratory instruments, always categorize them in your mind as either "Measuring/Detecting" or "Generating." Electroscopes, ammeters, and voltmeters are for detection/measurement, while Van de Graaff generators and Wimshurst machines are for producing charge.

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