2014 JAMB Physics Past Questions

Questions

1. 1.

   The energy in the nucleus of atoms produce heat which can be used to generate

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

   Show answer

   Answer: C. Electrical energy

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2. 2.

   The small droplets of water that form on the grass in the early hours of the morning is

   1. A.Fog
   2. B.Haul
   3. C.Mist
   4. D.Dew

   Show answer

   Answer: D. Dew

   AI explanation

   Analysis

   The question asks for the scientific term for the small water droplets that appear on grass during the early morning. This is a classic question on Thermal Physics, specifically focusing on the change of state and atmospheric conditions.

   Concept Explanation

   To understand this, we look at the concept of Condensation and the Dew Point:

   1. Water Vapor in the Air: The atmosphere always contains some amount of water vapor (invisible gas).
   2. Temperature Drop: During the night, the temperature of the air and the surfaces (like grass) drops significantly.
   3. Saturation: As the air cools, its ability to hold water vapor decreases. Eventually, the air reaches a temperature called the Dew Point, where it becomes saturated (it cannot hold any more water vapor).
   4. Condensation: When the temperature falls below the dew point, the excess water vapor in the air condenses into liquid water droplets on cool surfaces like grass, leaves, and metal. This phenomenon is known as Dew.

   Let's look at the other options to clarify why they are incorrect:

   • Fog/Mist: These are clouds of water droplets suspended in the air near the ground. They are not droplets on the grass, but rather a suspension in the atmosphere that reduces visibility.
   • Hail: This is a form of solid precipitation (ice pellets) that falls from clouds during thunderstorms, not a morning surface phenomenon.

   Step-by-Step Solution

   1. Identify the location of the droplets: The question specifies the droplets are on the grass.
   2. Identify the timing: The question specifies early hours of the morning (when temperatures are lowest).
   3. Apply the principle: The cooling of the earth's surface causes water vapor in the immediate vicinity to lose kinetic energy and change from gas to liquid (condensation).
   4. Match with terminology: The specific term for this condensation on surfaces is "Dew."

   Conclusion

   Based on the physical process of condensation occurring on surfaces due to cooling, the correct term is Dew.

   Exam Tip: Remember the "D-D-D" rule for this topic: Dew forms when the temperature drops to the Dew point, causing Deposition or condensation of water vapor.

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3. 3.

   What is the equivalent of 20K in Celsius scale?

   1. A.-253oC
   2. B.-293oC
   3. C.68oC
   4. D.36oC

   Show answer

   Answer: A. -253oC

   AI explanation

   Analysis

   The question asks for the conversion of a temperature value from the Kelvin (K) scale to the Celsius (°C) scale.

   Concept

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

   $T(^\circ\text{C}) = T(\text{K}) - 273.15$

   In most JAMB and secondary school physics contexts, we use the approximation:

   $T(^\circ\text{C}) = T(\text{K}) - 273$

   Solution

   1. Identify the given value: $T(\text{K}) = 20\text{K}$
   2. Apply the formula: $T(^\circ\text{C}) = 20 - 273$
   3. Calculate the result: $20 - 273 = -253$

   Therefore, 20K is equivalent to $-253^\circ\text{C}$.

   Conclusion

   Comparing our result to the provided options, it matches option A.

   Tip

   Always remember that the Kelvin scale is an "absolute scale," meaning it cannot have negative values (0K is absolute zero). When converting from Kelvin to Celsius, you subtract 273; when converting from Celsius to Kelvin, you add 273. A simple way to remember this is: "K is for Kelvin, and Kelvin is 'Kooler' (higher in value), so you add to get to Kelvin and subtract to get to Celsius."

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4. 4.

   The equation PaVbTc= constant reduces to Charles Law if

   1. A.a=1, b=1and c=0
   2. B.a=1, b=0 and c=-1
   3. C.a=0, b=1 and c=1
   4. D.a=0, b=1 and c=-1

   Show answer

   Answer: D. a=0, b=1 and c=-1

   AI explanation

   Analysis

   The question asks us to identify the values of the exponents $a, b,$ and $c$ in the general equation $P^a V^b T^c = \text{constant}$ that would transform it into Charles's Law.

   Concept: Charles's Law

   Charles's Law states that for a fixed mass of an ideal gas at constant pressure, the volume ($V$) is directly proportional to its absolute temperature ($T$).

   Mathematically, this is expressed as:

   $\frac{V}{T} = \text{constant}$

   Or, written in the form $V \cdot T^{-1} = \text{constant}$.

   Step-by-Step Solution

   1. Compare the equations: We are given the general form: $P^a V^b T^c = \text{constant}$. We want to reach the form: $V^1 T^{-1} = \text{constant}$.

   2. Match the variables: • To eliminate pressure ($P$), the exponent $a$ must be 0 (since $P^0 = 1$). • To match the volume ($V$), the exponent $b$ must be 1. • To match the temperature ($T$), the exponent $c$ must be -1 (since $T^{-1} = \frac{1}{T}$).

   3. Verify: Substituting $a=0, b=1, c=-1$ into the original equation: $P^0 \cdot V^1 \cdot T^{-1} = \text{constant}$ $1 \cdot V \cdot \frac{1}{T} = \text{constant}$ $\frac{V}{T} = \text{constant}$ This matches the definition of Charles's Law perfectly.

   Conclusion

   Comparing our findings ($a=0, b=1, c=-1$) with the given options, we see that it corresponds to option D.

   Exam Tip

   When dealing with gas law equations in JAMB, remember the "Constant" rule:

   • Boyle’s Law: Temperature is constant ($PV = k$) $\rightarrow a=1, b=1, c=0$.
   • Charles’s Law: Pressure is constant ($V/T = k$) $\rightarrow a=0, b=1, c=-1$.
   • Pressure Law: Volume is constant ($P/T = k$) $\rightarrow a=1, b=0, c=-1$.

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5. 5.

   One of the conditions necessary for an object to be in equilibrium when acted upon by a number of parallel forces is that the vector sum of the forces is

   1. A.Average
   2. B.Zero
   3. C.Negative
   4. D.Positive

   Show answer

   Answer: B. Zero

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6. 6.

   The focal length of a concave mirror is 2.0cm. If an object is placed 8.0cm from it, the image is at

   1. A.2.7m
   2. B.2.0m
   3. C.2.3m
   4. D.2.5m

   Show answer

   Answer: A. 2.7m

   AI explanation

   Analysis

   To solve this problem, we need to use the Mirror Formula, which relates the focal length ($f$), the object distance ($u$), and the image distance ($v$).

   Concept

   The mirror formula is given by:

   $\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$

   Where:

   • $f$ = focal length
   • $u$ = object distance
   • $v$ = image distance

   Note on Sign Convention: For a concave mirror, the focal length ($f$) is positive.

   Step-by-Step Solution

   1. Identify the given values:

   • Focal length ($f$) = 2.0 cm
   • Object distance ($u$) = 8.0 cm

   2. Rearrange the formula to solve for $v$:

   $\frac{1}{v} = \frac{1}{f} - \frac{1}{u}$

   3. Substitute the values into the equation:

   $\frac{1}{v} = \frac{1}{2.0} - \frac{1}{8.0}$

   4. Find a common denominator (which is 8.0):

   $\frac{1}{v} = \frac{4}{8.0} - \frac{1}{8.0}$

   $\frac{1}{v} = \frac{3}{8.0}$

   5. Solve for $v$:

   $v = \frac{8.0}{3}$

   $v = 2.666... \text{ cm}$

   Rounding to one decimal place, we get 2.7 cm.

   *Correction regarding the provided options:* The options provided in your question list the units as meters (m), but the calculation yields 2.7 cm. Given the context of JAMB questions, there is often a typographical error in the units of the options (using 'm' instead of 'cm'). Based on the numerical value, 2.7 matches option A.

   Exam Tip

   When dealing with mirror and lens problems, always remember the "Real is Positive" rule for mirrors:

   • Concave mirror: $f$ is positive.
   • Convex mirror: $f$ is negative.
   • If your final answer for $v$ is positive, the image is real and formed in front of the mirror. If $v$ is negative, the image is virtual and formed behind the mirror.

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7. 7.

   Which type of motion do the wheels of a moving car undergo?

   1. A.Vibratory and translational motion
   2. B.Random and translational motion
   3. C.Rotational mand oscillatory motion
   4. D.Translational and rotational motion

   Show answer

   Answer: D. Translational and rotational motion

   AI explanation

   Analysis of the Question

   The question asks us to identify the specific types of motion exhibited by the wheels of a car that is moving along a straight path.

   Concept Explanation

   To understand this, we need to define two specific types of motion:

   1. Translational Motion: This occurs when an object moves from one point to another in space. When a car moves along a road, the entire car (including its wheels) is moving forward. This forward movement is translational.
   2. Rotational Motion: This occurs when an object turns about a fixed axis. As the car moves, the wheels spin around their axles. This circular, spinning movement is rotational.

   When a wheel moves, it is simultaneously spinning (rotational) and moving forward with the car (translational). Therefore, the wheel undergoes both motions at the same time.

   Step-by-Step Solution

   1. Observe the car's movement: As the car travels down the road, the center of the wheel moves forward in a straight line. This is translational motion.
   2. Observe the wheel's movement: Simultaneously, the wheel spins around its axle to allow the car to move. This is rotational motion.
   3. Combine the observations: Since both motions happen concurrently, the wheels exhibit both translational and rotational motion.

   Evaluating the Options

   • A: Vibratory motion involves back-and-forth movement about a fixed point, which is not the primary motion of a car wheel.
   • B: Random motion is erratic and unpredictable, which does not describe the controlled movement of a car wheel.
   • C: Oscillatory motion is similar to vibratory motion; it is not the primary motion here.
   • D: This correctly identifies the combination of moving forward (translational) and spinning (rotational).

   Exam Tip

   Whenever you see a question about "rolling" objects (like a ball rolling down a hill or a wheel spinning on a car), always look for the combination of Translational (moving forward) and Rotational (spinning). This is a classic JAMB physics concept!

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8. 8.

   The distance between two successive crests of a wave is 15cm and the velocity 300$ms^{-1}$. Calculate the frequency.

   1. A.2.0x102Hz
   2. B.4.5x103Hz
   3. C.2.0x103Hz
   4. D.4.5x102Hz

   Show answer

   Answer: C. 2.0x103Hz

   AI explanation

   1. Analyze the question

   • Given: • Distance between two successive crests (Wavelength, $\lambda$) = $15\text{ cm}$ • Velocity ($v$) = $300\text{ ms}^{-1}$
   • To find: Frequency ($f$)

   2. Explain the concept

   In wave motion, the distance between two successive crests is defined as the wavelength ($\lambda$). The relationship between velocity, frequency, and wavelength is given by the wave equation:

   $v = f \times \lambda$

   Where:

   • $v$ is the velocity in meters per second ($\text{ms}^{-1}$)
   • $f$ is the frequency in Hertz ($\text{Hz}$)
   • $\lambda$ is the wavelength in meters ($\text{m}$)

   Important Note: Always ensure your units are consistent. Since velocity is in $\text{ms}^{-1}$, the wavelength must be converted from centimeters to meters.

   3. Show the solution

   Step 1: Convert wavelength to meters

   $\lambda = 15\text{ cm} = \frac{15}{100}\text{ m} = 0.15\text{ m}$

   Step 2: Rearrange the wave equation to solve for frequency ($f$)

   $f = \frac{v}{\lambda}$

   Step 3: Substitute the values

   $f = \frac{300}{0.15}$

   Step 4: Calculate the result To make the division easier, multiply both numerator and denominator by 100:

   $f = \frac{30000}{15}$

   $f = 2000\text{ Hz}$

   Step 5: Express in standard form

   $2000\text{ Hz} = 2.0 \times 10^3\text{ Hz}$

   4. Identify the answer

   Comparing our result to the given options, we find that $2.0 \times 10^3\text{ Hz}$ corresponds to option C.

   5. Tip

   Always check your units first! Many JAMB candidates lose marks because they forget to convert centimeters to meters. A quick way to remember: if the velocity is in meters, your wavelength must be in meters.

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9. 9.

   PHCN measures its electrical energy in

   1. A.W
   2. B.KWh
   3. C.Wh
   4. D.J

   Show answer

   Answer: B. KWh

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10. 10.

    A glass bottle of initial volume 2 x 10$^4$ cm$^3$ is heated from 20ºC to 50ºC. If the linear expansivity of glass is 9 x 10$^{-6}$K$^{-1}$, the volume of the bottle at 50ºC is

    1. A.20016.2cm3
    2. B.20005.4cm3
    3. C.20008.1cm3
    4. D.20013.5cm3

    Show answer

    Answer: A. 20016.2cm3

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11. 11.

    When a negatively charged rod is brought near the cap of a charged gold leaf electroscope which has positive charges, the leaf

    1. A.Remains the same
    2. B.Collapses
    3. C.Collapses and diverges again
    4. D.Diverges

    Show answer

    Answer: B. Collapses

    AI explanation

    Analysis

    This question tests your understanding of electrostatic induction and the behavior of charges in a gold leaf electroscope.

    Concept Explanation

    A gold leaf electroscope works on the principle that like charges repel.

    1. Initial State: The electroscope is positively charged, meaning the metal cap and the gold leaf have an excess of positive charges. Because they have the same charge, they repel each other, causing the leaf to diverge (stand away from the metal plate).
    2. The Interaction: When you bring a negatively charged rod near the cap, it exerts an electrostatic force on the charges in the electroscope.
    3. Neutralization: The negative rod attracts the positive charges from the leaf up towards the cap. As the positive charges move from the leaf to the cap, the amount of positive charge on the leaf decreases.
    4. Result: Since the leaf loses its positive charge, the repulsive force that was keeping it diverged weakens. Consequently, the leaf falls back toward the metal plate.

    Step-by-Step Solution

    1. Identify the initial state: The electroscope is positively charged, so the leaf is diverged.
    2. Apply the external influence: A negatively charged rod is brought near the cap.
    3. Analyze the charge movement: The negative rod attracts the positive charges in the electroscope toward the cap.
    4. Observe the effect on the leaf: As the positive charges leave the leaf to move toward the cap, the leaf becomes less positively charged (or neutral).
    5. Conclusion: With less charge on the leaf, the electrostatic repulsion decreases, causing the leaf to collapse.

    Identifying the Answer

    The leaf collapses because the negative rod neutralizes the positive charge on the leaf by attracting the positive charges toward the cap.

    Exam Tip

    Always remember the "Opposites Attract" rule in electrostatics. If the rod has the opposite charge to the electroscope, the leaf will collapse. If the rod had the same charge as the electroscope, the leaf would diverge further because the repulsion would increase!

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12. 12.

    What type of reaction is represented by the equation $^{2}_{1}X+^{2}_{1}X\rightarrow^{3}_{2}Y+^{1}_{0}n+Energy$

    1. A.Ionization
    2. B.Fusion
    3. C.Fission
    4. D.Chain

    Show answer

    Answer: B. Fusion

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13. 13.

    What is the best method of demagnetizing a steel bar magnet?

    1. A.Hammering
    2. B.Heating it
    3. C.Rough handling it
    4. D.Solenoid method

    Show answer

    Answer: D. Solenoid method

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14. 14.

    Which gas produces a red coloured light in a discharge tube?

    1. A.Mercury
    2. B.Argon
    3. C.Air
    4. D.Neon

    Show answer

    Answer: D. Neon

    AI explanation

    Analysis

    The question asks for the specific gas that emits a characteristic red-colored light when an electric discharge is passed through it in a vacuum or discharge tube.

    Concept Explanation

    When a high voltage is applied across a discharge tube containing a gas at low pressure, the gas atoms become excited. As these excited electrons return to their ground state, they release energy in the form of light (photons). The color of the light emitted is unique to the specific gas used because each element has a distinct energy level structure.

    • Mercury vapor: Typically produces a bluish-green or ultraviolet light (often used in fluorescent lamps).
    • Argon: Typically produces a pale lilac or violet light.
    • Air: Produces a pale blue or white glow.
    • Neon: Known for its distinct, brilliant reddish-orange glow, which is why it is widely used in "neon signs."

    Step-by-Step Solution

    1. Identify the phenomenon: This is an application of gas discharge physics, where different gases produce different emission spectra.
    2. Evaluate the options: • Mercury (A) is used in vapor lamps for white/blue light. • Argon (B) is an inert gas that glows violet/lilac. • Air (C) contains a mixture of gases, resulting in a faint blue/white glow. • Neon (D) is a noble gas that emits a bright red-orange light when ionized in a discharge tube.
    3. Conclusion: Based on the emission spectrum of noble gases, Neon is the correct gas that produces the red light.

    Exam Tip

    To remember this for your JAMB or WAEC exams, associate the word "Neon" directly with "Neon signs." If you have ever walked past a shop with bright red glowing signage, you are looking at the light produced by Neon gas!

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15. 15.

    When an atom undergoes a beta decay, the atomic number of the nucleus

    1. A.Remains unchanged
    2. B.Decreases by one
    3. C.Increases by one
    4. D.Becomes zero

    Show answer

    Answer: C. Increases by one

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16. 16.

    An object of weight 8kg on earth is taken to a planet where acceleration due to gravity is one-third of its value on earth. The weight of the object on the planet is

    1. A.48N
    2. B.12N
    3. C.27N
    4. D.36N

    Show answer

    Answer: C. 27N

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17. 17.

    Calculate the escape velocity of a satellite launched from the earth's surface if the radius of the earth is 6.4x106m

    1. A.25.3k$ms^{-1}$
    2. B.4.2k$ms^{-1}$
    3. C.4.0k$ms^{-1}$
    4. D.11.3k$ms^{-1}$

    Show answer

    Answer: D. 11.3k$ms^{-1}$

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18. 18.

    An object is placed 10m from a pinhole camera of length 25cm. Calculate the linear magnification.

    1. A.2.5x102
    2. B.2.5x10-2
    3. C.2.5x10-1
    4. D.2.5x101

    Show answer

    Answer: B. 2.5x10-2

    AI explanation

    1. Analyze the question

    We are given:

    • Object distance ($u$) = 10 m
    • Image distance/Camera length ($v$) = 25 cm
    • We need to find the linear magnification ($m$).

    2. Explain the concept

    In a pinhole camera, the magnification ($m$) is defined as the ratio of the image height to the object height, which is also equivalent to the ratio of the image distance ($v$) to the object distance ($u$).

    The formula is:

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

    Important Note: Before calculating, you must ensure that both distances are in the same unit. We will convert the object distance from meters (m) to centimeters (cm).

    3. Show the solution

    Step 1: Convert units

    • $u = 10 \text{ m} = 10 \times 100 \text{ cm} = 1000 \text{ cm}$
    • $v = 25 \text{ cm}$

    Step 2: Apply the formula

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

    $m = \frac{25}{1000}$

    Step 3: Simplify the fraction

    $m = \frac{25}{1000} = 0.025$

    Step 4: Express in standard form To convert $0.025$ to standard form: Move the decimal point 2 places to the right to get 2.5. Since we moved it 2 places to the right, we multiply by $10^{-2}$.

    $m = 2.5 \times 10^{-2}$

    4. Identify the answer

    Comparing our result to the given options: A. $2.5 \times 10^2$ B. $2.5 \times 10^{-2}$ C. $2.5 \times 10^{-1}$ D. $2.5 \times 10^1$

    The correct option is B.

    5. Tip

    Always check your units first! A very common mistake in JAMB Physics is forgetting to convert meters to centimeters or vice versa. If you had divided 25 by 10, you would have gotten 2.5, which would lead you to choose the wrong option. Always ensure your $u$ and $v$ are in the same units before dividing.

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19. 19.

    The magnitude of the angle of dip at the equator is

    1. A.360o
    2. B.0o
    3. C.90o
    4. D.180o

    Show answer

    Answer: B. 0o

    AI explanation

    Analysis

    The question asks for the angle of dip at the Earth's magnetic equator. The angle of dip (or magnetic inclination) is the angle that a freely suspended magnetic needle makes with the horizontal surface of the Earth.

    Concept Explanation

    • Magnetic Dip: This is the angle between the Earth's magnetic field lines and the horizontal plane.
    • At the Poles: The magnetic field lines are perpendicular to the Earth's surface. Therefore, a magnetic needle will point straight down (or up), resulting in an angle of dip of 90°.
    • At the Equator: The magnetic field lines are parallel to the Earth's surface. Because the field lines run horizontally, a freely suspended magnetic needle will remain perfectly horizontal. Since there is no vertical component to the magnetic field at the equator, the angle between the needle and the horizontal is 0°.

    Step-by-Step Solution

    1. Identify the location: We are looking at the Earth's equator.
    2. Determine the field orientation: At the equator, the Earth's magnetic field lines are horizontal.
    3. Relate to the needle: A magnetic needle aligns itself with the magnetic field lines. If the field is horizontal, the needle stays horizontal.
    4. Calculate the angle: The angle of dip is the angle between the horizontal and the needle. Since both are horizontal, the angle is 0°.

    Conclusion

    Exam Tip: Remember the mnemonic "E-Z": Equator = Zero degrees. Conversely, remember that the Poles are Perpendicular (90°). This will help you avoid mixing them up during your JAMB exam!

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20. 20.

    A circuit has a resistance of 200Ω. The resistance of the circuit can be reduced to 120Ω when

    1. A.A 300Ω resistor is connected to it in parallel
    2. B.An 80Ω resistor is conneceted to it in series
    3. C.A 150Ω resistor is connected to it in parallel
    4. D.A 240Ω resistor is connected to it in series

    Show answer

    Answer: A. A 300Ω resistor is connected to it in parallel

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21. 21.

    An object of mass 20kg is released from a height of 10m above the ground level. The kinetic energy of the object just before it hits the ground is

    1. A.200J
    2. B.4000J
    3. C.2000J
    4. D.500J

    Show answer

    Answer: C. 2000J

    AI explanation

    Analysis

    To solve this problem, we need to apply the Law of Conservation of Energy. This law states that energy cannot be created or destroyed, only transformed from one form to another. In this scenario, the object starts with Potential Energy (PE) at the top and converts it into Kinetic Energy (KE) as it falls.

    Concept

    • Potential Energy (PE): Energy possessed by an object due to its position. The formula is $PE = mgh$.
    • Kinetic Energy (KE): Energy possessed by an object due to its motion.
    • Conservation Principle: Just before the object hits the ground, all its initial potential energy has been converted into kinetic energy (ignoring air resistance). • Therefore: $KE_{final} = PE_{initial}$

    Step-by-Step Solution

    1. Identify the given values: • Mass ($m$) = $20\text{ kg}$ • Height ($h$) = $10\text{ m}$ • Acceleration due to gravity ($g$) = $10\text{ m/s}^2$ (Standard value used in JAMB physics unless otherwise specified).

    2. Calculate the initial Potential Energy: • $PE = m \times g \times h$ • $PE = 20\text{ kg} \times 10\text{ m/s}^2 \times 10\text{ m}$ • $PE = 2000\text{ J}$

    3. Relate to Kinetic Energy: • Since the object is released from rest, its initial kinetic energy is $0$. As it falls, the potential energy is converted entirely into kinetic energy. • $KE = 2000\text{ J}$

    Conclusion

    The kinetic energy of the object just before it hits the ground is equal to the potential energy it had at the height of 10m, which is 2000J.

    Exam Tip

    In JAMB Physics, whenever you see a question about an object falling from a height, don't waste time calculating velocity using equations of motion ($v^2 = u^2 + 2as$). Simply use the $PE = mgh$ formula. It is faster and less prone to calculation errors!

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22. 22.

    The maximum power transfer occur in a cell when the external resistance is

    1. A.Twice the internal resistance of the cell
    2. B.The same as the internal resistance of the cell
    3. C.Greater than the internal resistance of the cell
    4. D.Less than the internal resistance of the cell

    Show answer

    Answer: B. The same as the internal resistance of the cell

    AI explanation

    1. Analyze the Question

    The question asks for the condition under which a cell delivers the maximum amount of power to an external load (resistor). This is a classic application of the Maximum Power Transfer Theorem in electrical circuits.

    2. Explain the Concept

    In a simple circuit, a cell has an electromotive force ($E$) and an internal resistance ($r$). When you connect an external resistor ($R$) to this cell, the current ($I$) flowing through the circuit is given by Ohm's Law:

    $I = \frac{E}{R + r}$

    The power ($P$) dissipated by the external resistor $R$ is calculated using the formula:

    $P = I^2 R$

    Substituting the expression for $I$:

    $P = \left( \frac{E}{R + r} \right)^2 \times R = \frac{E^2 R}{(R + r)^2}$

    To find the value of $R$ that gives maximum power, we look for the point where the derivative of $P$ with respect to $R$ is zero ($\frac{dP}{dR} = 0$). Mathematically, this occurs when the external resistance $R$ is exactly equal to the internal resistance $r$.

    3. Show the Solution

    • Step 1: Identify the power formula: $P = \frac{E^2 R}{(R + r)^2}$
    • Step 2: Understand that for maximum power, the load resistance must match the source resistance. If $R$ is too small, the total current is high, but the voltage drop across the load is low. If $R$ is too large, the voltage drop is high, but the current is very low.
    • Step 3: The balance point where the product of current squared and resistance is maximized is when $R = r$.

    4. Identify the Answer

    Based on the derivation above, the maximum power transfer occurs when the external resistance is equal to the internal resistance of the cell.

    The correct option is B.

    5. Exam Tip

    Think of this like a "matching" game. To get the most "work" (power) out of a battery, the resistance of the device you are powering must "match" the internal resistance of the battery itself. If you ever forget this, remember that Maximum Power = Matching Resistance.

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23. 23.

    Which of the following is NOT a Fundamental S.I unit?

    1. A.Metre
    2. B.Ampere
    3. C.Newton
    4. D.Second

    Show answer

    Answer: C. Newton

    AI explanation

    Analysis

    The question asks us to identify which of the given units is not a fundamental S.I. unit. In physics, units are categorized into two types: Fundamental (Base) units and Derived units.

    Concept Explanation

    • Fundamental Units: These are the basic units of measurement that do not depend on any other units. There are seven base S.I. units: • Metre (length) • Kilogram (mass) • Second (time) • Ampere (electric current) • Kelvin (temperature) • Mole (amount of substance) • Candela (luminous intensity)
    • Derived Units: These are units formed by combining fundamental units through multiplication or division. For example, the unit for force (Newton) is derived from mass, length, and time ($F = ma$, so $1\text{ N} = 1\text{ kg}\cdot\text{m/s}^2$).

    Step-by-Step Solution

    1. Evaluate Option A (Metre): This is the base unit for length. It is a fundamental unit.
    2. Evaluate Option B (Ampere): This is the base unit for electric current. It is a fundamental unit.
    3. Evaluate Option C (Newton): This is the unit for force. As shown by the formula $F = ma$, it is defined as $\text{kg}\cdot\text{m/s}^2$. Since it is composed of other base units, it is a derived unit, not a fundamental one.
    4. Evaluate Option D (Second): This is the base unit for time. It is a fundamental unit.

    Conclusion

    Since the Newton is a derived unit (a combination of kilograms, metres, and seconds), it does not belong to the list of fundamental S.I. units.

    Exam Tip: To remember the seven fundamental units easily, use the mnemonic "L-M-T-A-K-M-C" (Length, Mass, Time, Ampere, Kelvin, Mole, Candela). If a unit is not on this list, it is almost certainly a derived unit!

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24. 24.

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

    1. A.0.1mm
    2. B.1.0mm
    3. C.0.5mm
    4. D.0.2mm

    Show answer

    Answer: C. 0.5mm

    AI explanation

    Analysis

    The question asks for the "least possible error" when using a meter rule. In physics, this is technically referred to as the uncertainty or the limit of reading accuracy of the instrument.

    Concept

    The limit of reading accuracy of any measuring instrument is generally taken as half of the smallest division on its scale.

    1. Smallest Division: A standard meter rule is calibrated in centimeters (cm) and millimeters (mm). The smallest division on a meter rule is 1 mm (or 0.1 cm).
    2. Calculation of Error: When you take a measurement, you can estimate the position of the object between the smallest markings. By convention, the smallest error (uncertainty) is half of the smallest scale division. • $\text{Error} = \frac{1}{2} \times (\text{smallest division})$ • $\text{Error} = \frac{1}{2} \times 1\text{ mm} = 0.5\text{ mm}$

    Solution

    • Step 1: Identify the smallest division on a meter rule, which is $1\text{ mm}$.
    • Step 2: Apply the rule for reading accuracy: $\text{Uncertainty} = \frac{1}{2} \times \text{smallest division}$.
    • Step 3: Calculate: $0.5 \times 1\text{ mm} = 0.5\text{ mm}$.

    Therefore, the least possible error (or the limit of accuracy) when using a meter rule is $0.5\text{ mm}$.

    Conclusion

    The correct option is C.

    Exam Tip

    Always remember the "Half-Division Rule":

    • Meter Rule: Smallest division = $1\text{ mm} \rightarrow$ Error = $0.5\text{ mm}$.
    • Vernier Caliper: Smallest division = $0.1\text{ mm} \rightarrow$ Error = $0.05\text{ mm}$.
    • Micrometer Screw Gauge: Smallest division = $0.01\text{ mm} \rightarrow$ Error = $0.005\text{ mm}$.

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25. 25.

    A wheel and an axle is used to raise a load whose weight is 800N when an effort of 250N is applied. If the radii of the wheel and axle are 800mm and 200mm respectively, the efficiency of the machine is

    1. A.90%
    2. B.80%
    3. C.85%
    4. D.87%

    Show answer

    Answer: B. 80%

    AI explanation

    Analysis

    To solve this problem, we need to calculate the Efficiency ($\eta$) of the machine. Efficiency is defined as the ratio of Mechanical Advantage (MA) to Velocity Ratio (VR), expressed as a percentage.

    Concept

    1. Mechanical Advantage (MA): This is the ratio of the Load ($L$) to the Effort ($E$). $$MA = \frac{L}{E}$$
    2. Velocity Ratio (VR): For a wheel and axle, this is the ratio of the radius of the wheel ($R$) to the radius of the axle ($r$). $$VR = \frac{R}{r}$$
    3. Efficiency ($\eta$): $$\eta = \left( \frac{MA}{VR} \right) \times 100\%$$

    Step-by-Step Solution

    Step 1: Identify the given values

    • Load ($L$) = 800 N
    • Effort ($E$) = 250 N
    • Radius of wheel ($R$) = 800 mm
    • Radius of axle ($r$) = 200 mm

    Step 2: Calculate the Mechanical Advantage (MA)

    $MA = \frac{800}{250} = 3.2$

    Step 3: Calculate the Velocity Ratio (VR)

    $VR = \frac{800}{200} = 4$

    Step 4: Calculate the Efficiency ($\eta$)

    $\eta = \left( \frac{3.2}{4} \right) \times 100\%$

    $\eta = 0.8 \times 100\%$

    $\eta = 80\%$

    Conclusion

    Comparing our result with the provided options, we find that the efficiency is 80%.

    Exam Tip

    When dealing with simple machines like the wheel and axle, always remember that Velocity Ratio is purely based on the dimensions (radii) of the machine, while Mechanical Advantage is based on the forces (load and effort). If your calculated efficiency is greater than 100%, you have likely swapped your MA and VR—go back and check your division!

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26. 26.

    A car accelerates uniformly from rest at 3$ms^{-2}$. its velocity after traveling a distance of 24m is

    1. A.12$ms^{-1}$
    2. B.144$ms^{-1}$
    3. C.72$ms^{-1}$
    4. D.36$ms^{-1}$

    Show answer

    Answer: A. 12$ms^{-1}$

    AI explanation

    Analysis

    To solve this problem, we need to identify the given parameters and select the appropriate kinematic equation that relates velocity, acceleration, and distance.

    Given parameters:

    • Initial velocity ($u$) = $0 \, ms^{-1}$ (since the car starts from rest)
    • Acceleration ($a$) = $3 \, ms^{-2}$
    • Distance ($s$) = $24 \, m$
    • Final velocity ($v$) = ?

    Concept

    Since we are dealing with uniform acceleration and we have distance, initial velocity, and acceleration, we use the third equation of motion:

    $v^2 = u^2 + 2as$

    Solution

    1. Substitute the known values into the formula: $$v^2 = (0)^2 + 2 \times 3 \times 24$$

    2. Perform the multiplication: $$v^2 = 0 + 6 \times 24$$ $$v^2 = 144$$

    3. Solve for $v$ by taking the square root of both sides: $$v = \sqrt{144}$$ $$v = 12 \, ms^{-1}$$

    Conclusion

    Comparing our result with the provided options, the correct velocity is $12 \, ms^{-1}$.

    Exam Tip

    Always check your units before starting. If the acceleration were in $km/h^2$ and distance in $km$, you would need to convert them to SI units ($m/s^2$ and $m$) before using the equations of motion. Also, remember that "from rest" always means $u = 0$, which simplifies your calculation significantly!

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27. 27.

    What charge is stored in a 0.1F capacitor when a 10V supply is connected across it?

    1. A.1C
    2. B.5C
    3. C.4C
    4. D.2C

    Show answer

    Answer: A. 1C

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28. 28.

    Calculate the mass of the copper deposited during electrolysis when a current of 4A passes through a copper salt for 2 hours. [Ece of Copper z=3.3x10-7kgC-1]

    1. A.2.9x105kg
    2. B.9.5x10-7kg
    3. C.9.5x10-3kg
    4. D.2.9x104kg

    Show answer

    Answer: C. 9.5x10-3kg

    AI explanation

    Analysis

    To solve this problem, we need to use Faraday’s First Law of Electrolysis, which states that the mass of a substance deposited during electrolysis is directly proportional to the quantity of electricity passed through the electrolyte.

    Concept

    The formula for calculating the mass ($m$) deposited is:

    $m = zIt$

    Where:

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

    Step-by-Step Solution

    1. Identify the given values:

    • Current ($I$) = $4\text{ A}$
    • Time ($t$) = $2\text{ hours}$
    • Electrochemical equivalent ($z$) = $3.3 \times 10^{-7}\text{ kg/C}$

    2. Convert time to SI units (seconds): Since there are 3,600 seconds in an hour:

    $t = 2 \times 3600\text{ s} = 7200\text{ s}$

    3. Substitute the values into the formula:

    $m = (3.3 \times 10^{-7}) \times 4 \times 7200$

    4. Perform the calculation:

    • First, multiply the current and time: $4 \times 7200 = 28,800\text{ C}$
    • Now, multiply by the Ece: $m = 3.3 \times 10^{-7} \times 28,800$
    • $m = 3.3 \times 10^{-7} \times 2.88 \times 10^4$
    • $m = (3.3 \times 2.88) \times 10^{-7+4}$
    • $m = 9.504 \times 10^{-3}\text{ kg}$

    Rounding to two significant figures, we get $9.5 \times 10^{-3}\text{ kg}$.

    Conclusion

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

    Exam Tip

    Always remember to convert time from hours or minutes to seconds before plugging it into the formula. Many students lose marks because they forget this conversion! Also, keep an eye on the units of the Ece provided in the question—if it is given in $\text{kg/C}$, your final answer will be in $\text{kg}$.

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29. 29.

    A force of 500N1 is applied to a steel wire of cross-sectional area 0.2m2, The tensile stress is

    1. A.2.5x104$Nm^{-2}$
    2. B.1.0x102$Nm^{-2}$
    3. C.1.0x103$Nm^{-2}$
    4. D.2.5x103$Nm^{-2}$

    Show answer

    Answer: D. 2.5x103$Nm^{-2}$

    AI explanation

    Analysis

    To solve this problem, we need to calculate the tensile stress acting on the steel wire. Stress is defined as the force applied per unit cross-sectional area of a material.

    Concept

    The formula for tensile stress ($\sigma$) is:

    $\text{Stress} = \frac{\text{Force} (F)}{\text{Area} (A)}$

    • Force ($F$): Measured in Newtons (N).
    • Area ($A$): Measured in square meters ($m^2$).
    • Unit of Stress: The SI unit is Newtons per square meter ($Nm^{-2}$) or Pascals (Pa).

    Solution

    Given the values from your question:

    • Force ($F$) = $500 \, \text{N}$
    • Area ($A$) = $0.2 \, \text{m}^2$

    Substitute these values into the formula:

    $\text{Stress} = \frac{500}{0.2}$

    To simplify the division, you can multiply both the numerator and the denominator by 10 to remove the decimal:

    $\text{Stress} = \frac{5000}{2}$

    $\text{Stress} = 2500 \, \text{Nm}^{-2}$

    Now, express $2500$ in standard form:

    $2500 = 2.5 \times 10^3 \, \text{Nm}^{-2}$

    The calculated value is $2.5 \times 10^3 \, \text{Nm}^{-2}$, which matches option D.

    Exam Tip

    When dealing with stress and pressure problems, always ensure your area is in square meters ($m^2$). If the question gives you the area in $cm^2$ or $mm^2$, you must convert it to $m^2$ first (e.g., $1 \, \text{cm}^2 = 10^{-4} \, \text{m}^2$) before dividing, otherwise, your answer will be incorrect!

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30. 30.

    The quantity of heat needed to raise the temperature of a body by 1K is the body's

    1. A.Heat capacity
    2. B.Internal energy
    3. C.Specific heat capacity
    4. D.Latent heat of fusion

    Show answer

    Answer: A. Heat capacity

    AI explanation

    Analysis

    The question asks for the definition of the physical quantity that describes the amount of heat energy required to increase the temperature of a specific object (a body) by 1 Kelvin (or 1 degree Celsius).

    Concept Explanation

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

    1. Heat Capacity ($C$): This is the quantity of heat required to raise the temperature of a whole body (regardless of its mass) by 1K or 1°C. Its unit is $J/K$. • Formula: $Q = C \Delta\theta$ (where $C$ is heat capacity).
    2. Specific Heat Capacity ($c$): This is the quantity of heat required to raise the temperature of a unit mass (usually 1kg) of a substance by 1K or 1°C. Its unit is $J/kg \cdot K$. • Formula: $Q = mc \Delta\theta$ (where $c$ is specific heat capacity).

    Since the question refers to "a body" (implying the object as a whole) rather than a "unit mass," we are referring to the heat capacity.

    Step-by-Step Solution

    • Step 1: Identify the variables. We are looking for the ratio of heat energy ($Q$) to the change in temperature ($\Delta\theta$).
    • Step 2: Apply the definition. The definition of heat capacity is $C = \frac{Q}{\Delta\theta}$.
    • Step 3: Evaluate the options. • A (Heat capacity): Matches the definition perfectly. • B (Internal energy): This is the total kinetic and potential energy of the molecules within the body, not the energy required to change its temperature. • C (Specific heat capacity): Requires the mass of the body to be specified (1kg). • D (Latent heat of fusion): This is the heat required to change the state of a substance from solid to liquid at a constant temperature, not to raise the temperature.

    Conclusion

    The correct term for the heat required to raise the temperature of a body by 1K is its heat capacity.

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31. 31.

    Heat transfer by convection in a liquid is due to the

    1. A.Latent heat of vaporization of the liquid
    2. B.Increased vibration of the molecules of the liquid about theit mean position
    3. C.Variation of density of the liquid
    4. D.Expansion of the liquid as it is heated

    Show answer

    Answer: C. Variation of density of the liquid

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32. 32.

    The temperature at which the water vapour present in the air is just sufficient to saturate air is

    1. A.Boiling point
    2. B.Ice point
    3. C.Saturation point
    4. D.Dew point

    Show answer

    Answer: D. Dew point

    AI explanation

    Analysis of the Question

    The question asks for the specific temperature at which the amount of water vapour currently in the air is enough to make that air fully saturated (i.e., at 100% relative humidity).

    Concept Explanation

    To understand this, we need to look at Humidity and Saturation:

    • Saturation: Air can hold a certain amount of water vapour depending on its temperature. Warmer air can hold more water vapour than cooler air.
    • Dew Point: This is the temperature to which a given sample of air must be cooled for the water vapour in it to become saturated. At this temperature, the air can no longer hold all the water vapour it contains, so the excess begins to condense into liquid water (dew, fog, or frost).
    • Boiling Point: This is the temperature at which the saturated vapour pressure of a liquid equals the external atmospheric pressure.
    • Ice Point: This is the temperature at which pure ice melts (0°C).

    Step-by-Step Solution

    1. Identify the state: The question specifies that the vapour present is "just sufficient to saturate the air."
    2. Relate to temperature: If we cool the air, its capacity to hold water vapour decreases. The temperature at which the current amount of vapour becomes the maximum amount the air can hold (saturation) is defined scientifically as the Dew Point.
    3. Evaluate the options: • A (Boiling point) relates to phase change from liquid to gas at high temperatures. • B (Ice point) relates to the freezing/melting point of water. • C (Saturation point) is a general term, not a specific temperature measurement. • D (Dew point) is the precise meteorological term for the temperature described in the question.

    Conclusion

    Exam Tip

    Think of the Dew Point as the "tipping point." If the temperature drops even slightly below the dew point, the air can no longer hold the moisture, and you get condensation (like dew on grass in the early morning). Remember: Dew Point = Condensation Temperature.

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33. 33.

    A quantity which requires magnitude and direction to be specified is

    1. A.Temperature
    2. B.Distance
    3. C.Displacement
    4. D.Mass

    Show answer

    Answer: C. Displacement

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34. 34.

    The melting point of a substance is equivalent to its

    1. A.Vapour Pressure
    2. B.Solidification Temperature
    3. C.Liquidification Temperature
    4. D.Solidification Pressures

    Show answer

    Answer: B. Solidification Temperature

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35. 35.

    When a telescope is in normal use, the final image is at

    1. A.Infinity
    2. B.The focus
    3. C.The radius of curvature
    4. D.The near point

    Show answer

    Answer: A. Infinity

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36. 36.

    A machine whose efficiency is 75% is used to lift a load of 1000N. Calculate the effort put in to the machine if it has a Velocity ratio of 4.

    1. A.343.32N
    2. B.233.33N
    3. C.333.33N
    4. D.334.33N

    Show answer

    Answer: C. 333.33N

    AI explanation

    1. Analyze the question

    We are given:

    • Efficiency ($\eta$): 75% (or 0.75)
    • Load ($L$): 1000 N
    • Velocity Ratio ($VR$): 4
    • Goal: Calculate the Effort ($E$)

    2. Explain the concept

    In simple machines, efficiency is defined as the ratio of Mechanical Advantage ($MA$) to Velocity Ratio ($VR$), expressed as a percentage:

    $\text{Efficiency} (\eta) = \frac{MA}{VR} \times 100\%$

    We also know that Mechanical Advantage is the ratio of Load to Effort:

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

    By combining these, we get the formula:

    $\eta = \frac{L}{E \times VR} \times 100\%$

    3. Show the solution

    Step 1: Write down the formula

    $\eta = \frac{L}{E \times VR}$

    (Note: Since we are using 0.75 for efficiency, we do not need to multiply by 100)

    Step 2: Rearrange the formula to solve for Effort ($E$)

    $E = \frac{L}{\eta \times VR}$

    Step 3: Substitute the given values

    $E = \frac{1000}{0.75 \times 4}$

    Step 4: Perform the calculation

    $E = \frac{1000}{3}$

    $E = 333.333... \text{ N}$

    4. Identify the answer

    Comparing our result to the options provided, the correct value is 333.33N. This matches option C.

    5. Exam Tip

    When dealing with machine problems, always remember that Efficiency is always less than 1 (or 100%) for real-life machines due to friction. If your calculated effort is lower than the load divided by the velocity ratio, you might have inverted your formula. Also, keep your units consistent—since the load is in Newtons, your effort will also be in Newtons.

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37. 37.

    When $^{210}_{82}Pb$ decays to $^{206}_{80}Pb$, it emits

    1. A.two alpha and two beta particles
    2. B.an alpha particle
    3. C.one beta particle
    4. D.one alpha and one beta particle

    Show answer

    Answer: B. an alpha particle

    AI explanation

    1. Analyze the question

    We are given a radioactive decay process where a parent nucleus, Lead-210 ($^{210}_{82}Pb$), transforms into a daughter nucleus, Lead-206 ($^{206}_{80}Pb$). We need to determine the type and number of particles emitted during this process.

    2. Explain the concept

    In nuclear physics, radioactive decay follows the Law of Conservation of Mass Number and the Law of Conservation of Atomic Number:

    • Mass Number ($A$): The total number of protons and neutrons must remain the same on both sides of the equation.
    • Atomic Number ($Z$): The total charge (number of protons) must remain the same on both sides of the equation.

    Particle characteristics:

    • Alpha particle ($\alpha$): Represented as $^{4}_{2}He$. It has a mass number of 4 and an atomic number of 2.
    • Beta particle ($\beta$): Represented as $^{0}_{-1}e$. It has a mass number of 0 and an atomic number of -1.

    3. Show the solution

    Let the decay equation be: $^{210}_{82}Pb \rightarrow ^{206}_{80}Pb + x(^4_2He) + y(^0_{-1}e)$

    Step 1: Calculate the change in Mass Number ($\Delta A$) $\Delta A = 210 - 206 = 4$ Since an alpha particle has a mass of 4, we divide the change by 4: $4 / 4 = 1$ alpha particle.

    Step 2: Calculate the change in Atomic Number ($\Delta Z$) $\Delta Z = 82 - 80 = 2$ If we emit 1 alpha particle, the atomic number decreases by 2 ($82 - 2 = 80$). Since the atomic number of the daughter nucleus is exactly 80, we do not need to emit any beta particles to balance the charge.

    Verification: $^{210}_{82}Pb \rightarrow ^{206}_{80}Pb + ^4_2He$

    • Mass: $206 + 4 = 210$ (Balanced)
    • Atomic: $80 + 2 = 82$ (Balanced)

    The decay process involves the emission of exactly one alpha particle.

    4. Identify the answer

    Comparing our result to the options provided, the correct choice is B.

    5. Tip

    When solving decay problems, always check the Mass Number first. If the mass number decreases by 4, it is a strong indicator of an alpha decay. If the mass number remains the same but the atomic number increases by 1, it is a beta decay.

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38. 38.

    A boy receives the echo of his clap reflected by a nearby hill 0.8s later. How far is he from the hill? [ speed of sound in air = $340ms^{-1}$

    1. A.528m
    2. B.66m
    3. C.136m
    4. D.264m

    Show answer

    Answer: C. 136m

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39. 39.

    I Electrical potential, II Torque, III Kinetic Energy, IV Momentum. Which of the quantities listed are vectors?

    1. A.II and IV
    2. B.I and II
    3. C.I and III
    4. D.II and III

    Show answer

    Answer: A. II and IV

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40. 40.

    What happens when three coplanar non-parallel forces are in equilibrium?

    1. A.Their lines of action are parallel.
    2. B.They are represented in magnitude only
    3. C.They are represented in direction only
    4. D.Their lines of action meet at a point

    Show answer

    Answer: D. Their lines of action meet at a point

    AI explanation

    Analysis

    The question asks for the geometric condition that must be satisfied for three coplanar (acting on the same plane) and non-parallel forces to be in equilibrium.

    Concept Explanation

    In physics, for an object to be in equilibrium under the influence of forces, two conditions must be met:

    1. Translational Equilibrium: The vector sum of all forces must be zero ($\sum F = 0$).
    2. Rotational Equilibrium: The sum of the moments (torques) about any point must be zero ($\sum \tau = 0$).

    When you have three coplanar, non-parallel forces acting on a body, the only way to ensure there is no rotation (the body doesn't spin) is if the lines of action of all three forces intersect at a single common point. If they did not meet at a point, the forces would create a resultant moment, causing the object to rotate.

    Step-by-Step Solution

    1. Visualize the forces: Imagine three forces, $F_1$, $F_2$, and $F_3$, acting on an object in the same plane.
    2. Check for rotation: If the lines of action of $F_1$ and $F_2$ intersect at a point $P$, the object will rotate around $P$ unless the third force $F_3$ also passes through that same point $P$.
    3. Apply the Triangle Law: When three forces are in equilibrium, they can be represented by the sides of a closed triangle taken in order. For this to hold true for non-parallel forces, their lines of action must be concurrent (meet at a single point).
    4. Evaluate the options: • A is incorrect because the forces are explicitly stated as "non-parallel." • B and C are incorrect because forces are vector quantities requiring both magnitude and direction. • D correctly describes the condition for rotational equilibrium for three coplanar forces.

    Conclusion

    Exam Tip

    Whenever you see a question about "three forces in equilibrium," immediately think of the Triangle of Forces. If the forces are coplanar and non-parallel, they must be concurrent (meeting at a point) to prevent the object from rotating. This is a classic JAMB concept, so keep it in your memory!

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41. 41.

    In a compound microscope, the objective and the eye piece focal lengths are

    1. A.At infinity
    2. B.Long
    3. C.Short
    4. D.The same

    Show answer

    Answer: C. Short

    AI explanation

    1. Analyze the Question

    The question asks for the characteristics of the focal lengths of the lenses used in a compound microscope. Specifically, it wants to know how the focal lengths of the objective lens and the eyepiece compare to each other.

    2. Explain the Concept

    A compound microscope is an optical instrument used to view very small objects. It consists of two converging (convex) lenses:

    • The Objective Lens: This lens is placed close to the object being viewed. To produce a highly magnified real image, the object must be placed just outside the focal point of this lens. Therefore, the objective lens must have a very short focal length.
    • The Eyepiece (Ocular): This lens acts as a simple magnifier for the image formed by the objective lens. To provide high magnification, it also requires a short focal length.

    In summary, both lenses in a compound microscope are designed to be short-focal-length lenses to achieve the high levels of magnification required for microscopy.

    3. Show the Solution

    • Step 1: Identify the purpose of the microscope. It is designed to magnify tiny objects.
    • Step 2: Recall the lens formula for magnification. Magnification is inversely proportional to the focal length ($M \approx \frac{L}{f_o} \times \frac{D}{f_e}$). To get a large magnification ($M$), the focal lengths of both the objective ($f_o$) and the eyepiece ($f_e$) must be small.
    • Step 3: Compare this to a telescope. In a telescope, the objective lens has a long focal length to gather light from distant objects, but in a microscope, we need high power, which necessitates short focal lengths for both lenses.

    4. Identify the Answer

    Based on the principles of optics, both the objective and the eyepiece of a compound microscope have short focal lengths.

    The correct option is C.

    5. Tip

    Memory Trick: Think of the word "Micro" (meaning small). Since a microscope is for "micro" things, remember that the lenses must be "short" (small focal lengths). Conversely, for a telescope (used for "macro" or distant things), the objective lens is "long."

    AI can make mistakes. Report anything that looks wrong.