The law of conservation of momentum is stated for closed and isolated system. What are the two conditions for a system to be closed and isolated?

A. No external force acts on the system and there is no change in mass of the system.

B. No external force acts on the system and there is a gain in mass.

C. No external force acts on the system and there is a loss in mass.

D. An external force acts on the system and there is no change in mass.

For a convex lens to form a real image, the distance between the object and the screen will be:

D. four times the focal length of the lens

A. equal to the focal length of the lens

B. less than the focal length of the lens

C. twice the focal length of the lens

D. four times the focal length of the lens

A convex mirror is used as a driving mirror; however, a disadvantage in this regard is that the image

D. appears farther away from the driver

C. is not as bright as we would like

D. appears farther away from the driver

The function of a fuse in an electric circuit is to

A. break the circuit when the current exceeds a certain value

B. save energy by reducing voltage

C. ensure that the current in the circuit exceeds a certain value

D. save energy by reducing the current

A capacitor described as a mica capacitor has

A. both plates are made of mica.

D. the same capacitance as that of mica

The capacitance of a parallel plate capacitor

D. is greater with dielectric between the plates than without dielectric.

A. decreases when the temperature between the plates decreases

B. increases when the potential difference between the plates is increased

C. is greater without a dielectric between the plates than with dielectric

D. is greater with dielectric between the plates than without dielectric.

All of the following uses are practical applications of x-ray except

B. determining the depth of a mine

D. detecting fractures in bones

Atmospheric pressure decreases with an increase in altitude because:

D. Interaction among air molecules decreases due to less quantity of air.

A. Acceleration due to gravity increases with altitude.

B. Temperature increases with altitude.

C. Internal energy increases with altitude.

D. Interaction among air molecules decreases due to less quantity of air.

In storing magnets, the keeper is used to

A. cancel the effect of the earth's magnetism

C. protect the magnet from stray electric field

D. increase the strength of the magnet.

Which of the following statements about a projectile is not correct?

C. The range of a projectile is independent of the acceleration due to gravity.

A. Projectile motion is a two-dimensional motion.

B. A projectile is an object launched into the air and allowed to move freely due to gravity.

C. The range of a projectile is independent of the acceleration due to gravity.

D. The time of flight dependent of the acceleration due to gravity

To convert a milli-ammeter to an ammeter, a resistor of low value is necessary to connect a resistor of

C. low value in parallel with it

B. high value in series with it

C. low value in parallel with it

D. high value in parallel with it

Which of the following modes is the most economical method of transmitting electrical power over a long distance?

A. Alternating current at high voltage and low current.

B. Alternating current at low voltage and high current.

C. Direct current at high voltage and low current.

D. Direct current at low voltage and high current.

The vacuum and silvered wall surfaces of a vacuum flask walls are respectively

B. prevent conduction and convection and minimize radiation

A. minimize conduction and convection and prevent radiation

B. prevent conduction and convection and minimize radiation

C. prevent conduction and minimize convection and radiation

D. minimize convection and prevent conduction and radiation

Which of the following terms has different dimension from the others?

C. $\frac{\text{stress}}{\text{strain}}$

The magnitude of the acceleration of a moving object is equal to the

B. gradient of a velocity-time graph

A. gradient of a displacement-time graph

B. gradient of a velocity-time graph

C. area below a force-time graph

D. area below a velocity-time graph

A ray of light travels from a less dense medium to a denser medium. How are the speed and frequency of the light affected? The speed

D. decreases and the frequency remains the same

A. Increases and the frequency increases

B. decreases and the frequency decreases

C. increases and the frequency remains the same

D. decreases and the frequency remains the same

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

A. Concave mirror of focal length 5cm.

B. Concave mirror of focal length 10 cm.

C. Convex mirror of focal length 10 cm

D. Convex mirror of focal length 5cm

Chromatic aberration in lenses can be corrected by using a combination of

A. diverging and converging lenses.

B. an opaque material to cover the rims of lenses.

C. wide parallel beams on the lenses' surface.

A body moves with uniform velocity when the resultant force on it is

A. greater than the frictional force acting on it

B. less than the frictional force acting on it

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WAEC (WASSCE) 2024

2024 WAEC (WASSCE) Physics Past Questions and Answers

The 2024 WAEC (WASSCE) Physics past questions with answers: 50 objective questions from the 2024 paper in the DeeepSolve question bank, each with its answer behind "Show answer". Try each question before you check, then practise the paper as a timed WAEC-style CBT.

Practise this paper as a timed WAEC-style CBT All WAEC (WASSCE) Physics years

Questions

1.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.
2.
A constant voltage source supplies a sinusoidal alternating e.m.f. The voltage marked against the components are their peak values. Determine the peak value of the applied e.m.f
1. A.1V
2. B.4V
3. C.5V
4. D.2V
Show answer
Answer: C. 5V
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3.
An object is placed 1.5 m from a plane mirror. How far is the image from the object?
1. A.3.0 m
2. B.1.3 m
3. C.1.0 m
4. D.0.3 m
Show answer
Answer: A. 3.0 m
AI explanation
Analyze the question: An object stands 1.5 m in front of a plane mirror. We need the distance between the object and its image (not the distance from the mirror to the image).
Concept: A plane mirror forms a virtual image that is the same distance behind the mirror as the object is in front of it.
Object distance = image distance
u = v
Solution:
Object distance from mirror = 1.5 m
Image distance behind mirror = 1.5 m
Distance from object to image = object distance + image distance
= 1.5 m + 1.5 m = 3.0 m
Answer: A. 3.0 m
Tip: Read the question carefully to see what distance is being asked for. If it asks "how far is the image from the mirror?", the answer is 1.5 m. If it asks "how far is the image from the object?", double it. Examiners love this trap, and options like 1.5 m are often used to catch careless students.
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4.
The law of conservation of momentum is stated for closed and isolated system. What are the two conditions for a system to be closed and isolated?
1. A.No external force acts on the system and there is no change in mass of the system.
2. B.No external force acts on the system and there is a gain in mass.
3. C.No external force acts on the system and there is a loss in mass.
4. D.An external force acts on the system and there is no change in mass.
Show answer
Answer: A. No external force acts on the system and there is no change in mass of the system.
AI explanation
Step 1: Analyze the question The question asks for the two conditions that make a system "closed and isolated" for the law of conservation of momentum to apply.
Step 2: The concept
Isolated system: No net external force acts on it. Without an external force, nothing from outside can change the system's total momentum.
Closed system: No mass enters or leaves, so the total mass stays constant. If mass were gained or lost, it would carry momentum into or out of the system.
The law of conservation of momentum states: the total momentum of a closed, isolated system remains constant.
Step 3: Check each option
A. No external force and no change in mass. This matches both conditions, so it is correct.
B. A gain in mass means the system is not closed, so it is wrong.
C. A loss in mass means the system is not closed, so it is wrong. (A rocket expelling fuel is an example.)
D. An external force means the system is not isolated, so it is wrong.
Step 4: Answer The correct option is A: no external force acts on the system and there is no change in mass of the system.
Tip: Remember "Isolated = no Impulse from outside forces" and "Closed = no Change in mass." Both must hold for momentum to be conserved.
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5.
An object 2.0 cm high is placed at the radius of curvature of a concave mirror such that it is perpendicular to the principal axis of the mirror. Determine the height of the image.
1. A.0.5 cm
2. B.1.0 cm
3. C.1.5 cm
4. D.2.0 cm
Show answer
Answer: D. 2.0 cm
AI explanation
Analyze the question: The object is placed at the radius of curvature (u = R = 2f) of a concave mirror. We need the image height. Concept: The mirror formula is 1/f = 1/u + 1/v, and magnification is m = v/u = h_i/h_o (ignoring the sign, which only tells us the image is inverted). Solution: Since the object is at the radius of curvature, u = R = 2f. 1/v = 1/f − 1/u 1/v = 1/f − 1/(2f) 1/v = (2 − 1)/(2f) = 1/(2f) So v = 2f, which means the image forms at the centre of curvature too. Magnification: m = v/u = 2f/2f = 1 Image height: h_i = m × h_o = 1 × 2.0 cm = 2.0 cm Nature of the image: real, inverted, and the same size as the object, located at C (the centre of curvature). Answer: The image height is 2.0 cm, which is option D. Exam tip: Remember the special case for a concave mirror: when the object is at C (2f), the image is at C, real, inverted, and the same size (m = 1). Whenever a question says "placed at the radius of curvature," think "same size." The image height will equal the object height.
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6.
The amount of heat energy that will be extracted when 0.02kg of water vapor condenses to water at 97ºC is [specific heat capacity of water = 4200Jkg $^{-1}$ k $^{-1}$ , Specific heat of vaporization of water = 2.26 x 10 $^6$ Jkg $^{-1}$ ]
1. A.45,452J
2. B.45,200J
3. C.25,200J
4. D.252J
Show answer
Answer: A. 45,452J
AI explanation
Analyze the question: Water vapour condenses to water at 97°C. We need the heat extracted. The question is ambiguous, so first work out what the data supports.
Concept: Heat released during condensation is Q = mL, where L is the specific latent heat of vaporization.
Calculation: Q = mL = 0.02 × 2.26 × 10⁶ = 45,200 J
That matches option B exactly.
Checking option A (45,452 J): 45,452 − 45,200 = 252 J. This is 0.02 × 4200 × 3 = 252 J, which is the heat released when the water cools by 3°C, from 100°C to 97°C.
So the full process is:
Vapour at 100°C condenses to water at 100°C: 45,200 J
Water cools from 100°C to 97°C: mcΔθ = 0.02 × 4200 × 3 = 252 J
Total = 45,200 + 252 = 45,452 J
Which reading is right? The question says the vapour condenses to water at 97°C. This means the final water is at 97°C, so the vapour (at its boiling point of 100°C) condenses and then the water cools down to 97°C. The cooling step must therefore be included, and the total is 45,452 J.
Answer: A (45,452 J)
Tip: When a question gives the specific heat capacity of water as well as the latent heat, check for a temperature change as well as a phase change. Steam condensing at 100°C and then cooling to a lower temperature needs both Q = mL and Q = mcΔθ. If the specific heat capacity is supplied, it is usually meant to be used.
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7.
For a convex lens to form a real image, the distance between the object and the screen will be:
1. A.equal to the focal length of the lens
2. B.less than the focal length of the lens
3. C.twice the focal length of the lens
4. D.four times the focal length of the lens
Show answer
Answer: D. four times the focal length of the lens
AI explanation
The question is about the distance between the object and the screen when a convex lens forms a real image. The usual textbook result is that this distance must be at least four times the focal length. The options don't say "at least," so we need to read the wording carefully.
Step 1: Analyze the question We need the condition on the object-to-screen distance D for a real image to form on a screen.
Step 2: The concept Use the lens formula:
1/f = 1/u + 1/v
Here u is the object distance and v is the image distance. Both are positive for a real object and a real image. The object-to-screen distance is D = u + v.
Step 3: Derivation From the lens formula, v = uf / (u − f).
So D = u + uf/(u − f) = u² / (u − f).
Rearranging gives a quadratic in u:
u² − Du + Df = 0
For u to be real (so the lens can be placed somewhere to form a sharp image), the discriminant must be non-negative:
D² − 4Df ≥ 0 D(D − 4f) ≥ 0 D ≥ 4f
Step 4: Interpret
If D < 4f, no real image can form on the screen.
If D = 4f, there is exactly one position, with u = v = 2f. The image is the same size as the object.
If D > 4f, there are two possible lens positions.
So A, B and C are all impossible. A and B give a distance less than 4f, and C gives 2f, which is also less than 4f. Only D, four times the focal length, matches the condition. It is the minimum distance, and strictly it means "at least four times."
Answer: D. four times the focal length of the lens.
Tip: Remember "minimum object-to-screen distance = 4f." This is the case where u = v = 2f, so the image is real, inverted and the same size as the object. Many exam questions on this topic are really asking for this minimum.
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8.
A convex mirror is used as a driving mirror; however, a disadvantage in this regard is that the image
1. A.it produces is virtual
2. B.it produces is real
3. C.is not as bright as we would like
4. D.appears farther away from the driver
Show answer
Answer: D. appears farther away from the driver
AI explanation
Analyze the question A convex (diverging) mirror is used as a driving mirror because it gives a wide field of view. The question asks for a disadvantage of the image it forms.
Explain the concept A convex mirror always forms an image that is:
virtual (it appears behind the mirror)
upright
diminished (smaller than the object)
Because the image is diminished, objects look smaller, and so they seem farther away than they really are. This is the real drawback. A driver may misjudge the distance of vehicles behind and think they are farther than they actually are.
Check each option
A. The image is virtual: This is true, but it is not a disadvantage. A driver only needs to see the image, and a virtual image is perfectly good for that.
B. The image is real: This is false. A convex mirror cannot form a real image of a real object.
C. The image is not as bright: This is not the standard disadvantage. The image brightness is not the reason given for the mirror's limitation.
D. The image appears farther away from the driver: This is correct. The diminished image makes vehicles seem more distant than they are, which can cause misjudgment.
Answer: D.
Tip: Remember "convex = wide view, small image." Wide view is the advantage, and the small image that makes things look far away is the disadvantage. Similar questions often ask why convex mirrors are used for driving mirrors, shop security mirrors, or street corners. The answer is always the wider field of view.
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9.
The function of a fuse in an electric circuit is to
1. A.break the circuit when the current exceeds a certain value
2. B.save energy by reducing voltage
3. C.ensure that the current in the circuit exceeds a certain value
4. D.save energy by reducing the current
Show answer
Answer: A. break the circuit when the current exceeds a certain value
AI explanation
Step 1: Analyze the question The question asks about the purpose of a fuse in a circuit. This is a basic electricity and safety concept.
Step 2: The concept A fuse is a safety device containing a thin wire made of a material with a low melting point (such as tin-lead alloy). It is connected in series with the appliance or circuit it protects.
Under normal conditions, the current is within the safe rating, and the wire stays intact.
If the current becomes too large (due to a short circuit or overload), the heating effect of the current (H = I²Rt) makes the wire get hot, melt, and break the circuit.
This stops the flow of current and prevents damage to appliances, overheating of wires, and fire.
Step 3: Evaluate each option
A. Break the circuit when the current exceeds a certain value. Correct. This is exactly what a fuse does.
B. Save energy by reducing voltage. Wrong. A fuse does not change voltage or save energy. Transformers change voltage.
C. Ensure that the current exceeds a certain value. Wrong. This is the opposite of a fuse's purpose, because it protects against excess current.
D. Save energy by reducing the current. Wrong. A fuse does not regulate or reduce current. It simply cuts it off when it is too high.
Step 4: Answer
Tip: Think "fuse = safety valve." It sacrifices itself (melts) to protect the circuit. Also remember that a fuse is always connected in the live wire, in series with the appliance. In calculations, choose a fuse rating slightly higher than the normal working current (I = P/V). For example, a 1000 W appliance on 240 V draws about 4.2 A, so a 5 A fuse is suitable.
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10.
A cube of water with side 10.0 cm floats vertically in water with 4.5 cm its length submerged. Calculate the density of the wood. [Density of water = 1 g/cm $^3$ ; D = 0.090 g/cm $^3$ ]
1. A.0.090 g/cm $^3$
2. B.0.450 g/cm $^3$
3. C.0.230 g/cm $^3$
4. D.0.0450 g/cm $^3$
Show answer
Answer: B. 0.450 g/cm $^3$
AI explanation
Analyze the question: The question says "cube of water", but it is clearly meant to be a cube of wood, since we are asked for the density of the wood. The cube has side 10.0 cm and floats with 4.5 cm of its height submerged in water.
Concept: A floating body obeys the law of flotation: weight of the body = weight of the water displaced (upthrust).
Weight of cube = ρ_wood × V_cube × g
Upthrust = ρ_water × V_submerged × g
Solution:
Cross-sectional area A = 10 × 10 = 100 cm²
V_cube = 100 × 10 = 1000 cm³
V_submerged = 100 × 4.5 = 450 cm³
Equating weight and upthrust:
ρ_wood × 1000 = 1 × 450
ρ_wood = 450 / 1000 = 0.45 g/cm³
Equivalently, ρ_wood = (submerged depth / total height) × ρ_water = (4.5/10) × 1 = 0.45 g/cm³.
Note on the "D = 0.090 g/cm³" in the question: This value is not needed for the calculation and appears to be a leftover from the original question (possibly relating to another part). The result from the flotation principle is 0.
Answer: B. 0.450 g/cm³
Tip: For any floating object, the fraction submerged equals the ratio of the object's density to the liquid's density. Here, 4.5/10 = 0.45 of the cube is under water, so the wood's density is 0.45 times that of water.
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11.
A temperature of 60º C is equivalent to
1. A.25ºF
2. B.140ºF
3. C.50ºF
4. D.108ºF
Show answer
Answer: B. 140ºF
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12.
A capacitor described as a mica capacitor has
1. A.both plates are made of mica.
2. B.a mica dielectric.
3. C.a dielectric made of mica
4. D.the same capacitance as that of mica
Show answer
Answer: A. both plates are made of mica.
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13.
Light of energy 1.12 x 10 $^{-18}$ J is incident on a metal of ejected electrons with maximum energy of 8.0 x 10 $^{-19}$ J. Calculate the threshold frequency of the metal. [h = 6.626 x 10 $^{-34}$ Js]
1. A.4.8 x 10 $^{14}$ Hz
2. B.1.2 x 10 $^{15}$ Hz
3. C.1.7 x 10 $^{15}$ Hz
4. D.2.8 x 10 $^{15}$ Hz
Show answer
Answer: A. 4.8 x 10 $^{14}$ Hz
AI explanation
Analyze the question: This is a photoelectric effect problem. Light of energy E falls on a metal and the ejected electrons have a maximum kinetic energy. We need the threshold frequency f₀.
Concept: Einstein's photoelectric equation:
E = W₀ + KE_max, where W₀ = hf₀ (the work function)
So hf₀ = E − KE_max
Solution:
Work function: W₀ = 1.12 × 10⁻¹⁸ − 8.0 × 10⁻¹⁹ W₀ = 11.2 × 10⁻¹⁹ − 8.0 × 10⁻¹⁹ = 3.2 × 10⁻¹⁹ J
Threshold frequency: f₀ = W₀ / h = (3.2 × 10⁻¹⁹) / (6.626 × 10⁻³⁴) f₀ ≈ 0.483 × 10¹⁵ Hz ≈ 4.8 × 10¹⁴ Hz
Tip: Always write the energy values with the same power of ten (for example, 11.2 × 10⁻¹⁹ and 8.0 × 10⁻¹⁹) before subtracting. This avoids the most common slip in this type of question. Also remember: photon energy = work function + maximum kinetic energy.
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14.
Two isolated charged spheres each of magnitude + 1.0 x 10 $^{-6}$ C are seperated by a distance of 2.0 x 10 $^{-1}$ m. Calculate the magnitude of the electrostatic force between them [K = $\frac{1}{4\pi \epsilon_o}$ = 9 x 10 $^9$ Nm $^2$ C $^{-2}$ ]
1. A.2.25 x 10 $^{-1}$ N
2. B.4.50 x 10 $^{-1}$ N
3. C.2.25 x 10 $^1$ N
4. D.4.50 x 10 $^1$ N
Show answer
Answer: A. 2.25 x 10 $^{-1}$ N
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15.
The capacitance of a parallel plate capacitor
1. A.decreases when the temperature between the plates decreases
2. B.increases when the potential difference between the plates is increased
3. C.is greater without a dielectric between the plates than with dielectric
4. D.is greater with dielectric between the plates than without dielectric.
Show answer
Answer: D. is greater with dielectric between the plates than without dielectric.
AI explanation
Step 1: Analyze the question We need to find the true statement about the capacitance of a parallel plate capacitor.
Step 2: The concept For a parallel plate capacitor:
C = ε₀εᵣA / d
A = area of the plates
d = separation between the plates
εᵣ = relative permittivity (dielectric constant) of the material between the plates
For a vacuum or air, εᵣ ≈ 1. For any dielectric, εᵣ > 1.
Capacitance depends only on the geometry (A and d) and the material between the plates (εᵣ). It does not depend on the charge or the potential difference.
Step 3: Check each option
A. Decreases when temperature decreases. Temperature is not a factor in the formula, so this is not the standard answer. ✗
B. Increases when p.d. increases. Capacitance is a constant for a given capacitor. Increasing V increases the charge Q proportionally (C = Q/V), but C stays the same. ✗
C. Greater without a dielectric. This is the opposite of the truth. Removing the dielectric sets εᵣ = 1, which lowers C. ✗
D. Greater with a dielectric than without. Since εᵣ > 1 for a dielectric, C = ε₀εᵣA/d is larger than the value without it. ✓
Step 4: Answer The correct option is D.
Tip: Remember "dielectric = bigger capacitance." The dielectric reduces the effective electric field between the plates, so the plates can hold more charge for the same voltage. Also remember that C never depends on Q or V. It depends only on A, d and the dielectric.
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16.
All of the following uses are practical applications of x-ray except
1. A.the treatment of tumors
2. B.determining the depth of a mine
3. C.dental operation
4. D.detecting fractures in bones
Show answer
Answer: B. determining the depth of a mine
AI explanation
Analyze the question: We need the one use that is NOT an application of X-rays.
Concept: X-rays are high-energy electromagnetic waves with very short wavelengths. They penetrate soft tissue but are absorbed by dense materials such as bone. This gives them these practical uses:
Medical imaging: detecting bone fractures, dental X-rays, and checking for foreign objects.
Radiotherapy: high-energy X-rays destroy cancerous cells in tumors.
Industrial use: checking for cracks in metals and welds, and airport baggage scanning.
Crystallography: studying the structure of crystals.
Checking each option:
A. Treatment of tumors: Yes. This is radiotherapy.
B. Determining the depth of a mine: No. X-rays can't measure depth underground. Depth is found by methods such as sonar or echo-sounding (using sound waves), ropes and measuring lines, or surveying and seismic techniques.
C. Dental operation: Yes. Dental X-rays are used to examine teeth and roots.
D. Detecting fractures in bones: Yes. This is the most common use of X-rays.
Tip: For "all of the following except" questions, check each option against the known uses. X-rays are linked to imaging, medical treatment, and material inspection. Measuring depth or distance usually points to sound (echo) or radar, not X-rays.
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17.
Atmospheric pressure decreases with an increase in altitude because:
1. A.Acceleration due to gravity increases with altitude.
2. B.Temperature increases with altitude.
3. C.Internal energy increases with altitude.
4. D.Interaction among air molecules decreases due to less quantity of air.
Show answer
Answer: D. Interaction among air molecules decreases due to less quantity of air.
AI explanation
Analyze the question: We are asked why atmospheric pressure drops as we go higher above the earth's surface.
Explain the concept: Atmospheric pressure at any point is caused by the weight of the air column above that point. It is also related to how often air molecules collide with a surface and how hard they hit it.
At sea level, a tall column of air lies above you, so the pressure is high.
As you climb, less air remains above you, so there is less weight pressing down.
The air also becomes less dense at higher altitude. There are fewer molecules per unit volume, so there are fewer collisions and less interaction among them.
Check each option:
A. Acceleration due to gravity increases with altitude. False. Gravity actually decreases very slightly with altitude, and that is not the main reason for the drop in pressure.
B. Temperature increases with altitude. False. In the lower atmosphere (the troposphere, where we live and climb mountains), temperature decreases with altitude. In any case, temperature is not the reason for the pressure drop.
C. Internal energy increases with altitude. False. This has no basis as the cause of lower pressure.
D. Interaction among air molecules decreases due to less quantity of air. This is the best option. Higher up, there is less air, so fewer molecules and fewer collisions, and the pressure is lower.
Answer: D. It is the only option that describes the real cause: there is less air at higher altitude.
Tip: Remember "higher up, less air above, less pressure." For any WASSCE question on pressure variation, think of the weight or amount of fluid above the point. The same idea explains why pressure increases with depth in liquids. Also remember that gravity decreases slightly with height, so any option claiming it increases is wrong.
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18.
In storing magnets, the keeper is used to
1. A.cancel the effect of the earth's magnetism
2. B.reduce self demagnetization
3. C.protect the magnet from stray electric field
4. D.increase the strength of the magnet.
Show answer
Answer: B. reduce self demagnetization
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19.
Which of the following statements about a projectile is not correct?
1. A.Projectile motion is a two-dimensional motion.
2. B.A projectile is an object launched into the air and allowed to move freely due to gravity.
3. C.The range of a projectile is independent of the acceleration due to gravity.
4. D.The time of flight dependent of the acceleration due to gravity
Show answer
Answer: C. The range of a projectile is independent of the acceleration due to gravity.
AI explanation
Step 1: Analyze the question We are asked to find the statement that is NOT correct about a projectile.
Step 2: Key concepts For a projectile launched with speed u at angle θ:
Time of flight: T = 2u sinθ / g
Range: R = u² sin2θ / g
Maximum height: H = u² sin²θ / 2g
Motion has a horizontal part (constant velocity) and a vertical part (acceleration g downward), so it is two-dimensional.
Step 3: Check each option
A. Projectile motion is two-dimensional (horizontal and vertical). Correct.
B. A projectile is an object launched into the air and moves freely under gravity. Correct. This is the standard definition.
C. "The range is independent of g." From R = u² sin2θ / g, the range is inversely proportional to g, so it depends on g. This statement is false.
D. "The time of flight depends on g." From T = 2u sinθ / g, this is true, so the statement is correct (despite the grammar slip).
Step 4: Conclusion The statement that is not correct is C.
Tip: Notice that g appears in the denominator of T, R, and H formulas. So if a statement says any of these is independent of g, it is almost certainly wrong. On the Moon (smaller g), a projectile would travel much farther and stay up longer.
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20.
Which of the following factors does not affect the speed of sound?
1. A.Loudness.
2. B.Wind direction
3. C.Temperature
4. D.Material density
Show answer
Answer: A. Loudness.
AI explanation
Analyze the question: We need the factor that does NOT change how fast sound travels.
Concept: The speed of sound depends on the properties of the medium it travels through, not on properties of the sound wave itself, such as loudness (amplitude) or, in most cases, frequency.
For a gas, v = √(γRT/M), so speed depends on:
Temperature: Higher temperature makes molecules move faster, so sound travels faster (about 331 m/s at 0°C, rising roughly 0.6 m/s per °C).
Density and elasticity of the medium: In general, v = √(elastic modulus / density). Sound travels faster in solids than in liquids, and faster in liquids than in gases, mainly because of differences in elasticity.
Wind (motion of the medium): If the air moves in the direction of the sound, the effective speed relative to the ground increases. If it moves against the sound, the effective speed decreases.
Check each option:
A. Loudness: Loudness depends on amplitude (energy). A loud shout and a whisper travel at the same speed in the same air. It does not affect speed.
B. Wind direction: It changes the effective speed of sound relative to the ground, so it affects speed.
C. Temperature: It affects speed, as shown above.
D. Material density: It affects speed, since v depends on density and elasticity of the medium.
Answer: The factor that does not affect the speed of sound is A. Loudness.
Exam tip: Remember that speed depends on the medium (temperature, density, elasticity, wind), not on the source or wave features (loudness, pitch or frequency). If a question asks which does not affect speed, look for loudness or amplitude.
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21.
A particle of mass 3.6 x 10 $^{-6}$ kg revolving around the earth has a radial acceleration of 4.3 x 10 $^7$ ms $^{-2}$ . Calculate the centripetal force of the particle.
1. A.1.55 x 10 $^2$ N
2. B.2.00 x 10 $^{-2}$ N
3. C.6.25 x 10 $^{-14}$ N
4. D.1.00 x 10 $^2$ N
Show answer
Answer: A. 1.55 x 10 $^2$ N
AI explanation
Analyze the question We are given the mass and the radial (centripetal) acceleration, and we need the centripetal force.
Concept Centripetal force is given by Newton's second law applied to circular motion:
F = m × a
where a is the radial (centripetal) acceleration.
Solution
m = 3.6 × 10⁻⁶ kg
a = 4.3 × 10⁷ m/s²
F = (3.6 × 10⁻⁶) × (4.3 × 10⁷) F = (3.6 × 4.3) × 10^(−6+7) F = 15.48 × 10¹ F = 154.8 N ≈ 1.55 × 10² N
Answer
Tip When multiplying numbers in standard form, multiply the coefficients and add the powers of 10. Here 3.6 × 4.3 = 15.48 and the powers give 10¹, so the answer is about 155 N. Also, if a question gives mass and acceleration, you don't need the radius or speed. Just use F = ma.
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22.
Water is readily available but it is not a thermometric liquid mainly because
1. A.clings to glass
2. B.does not expand uniformily
3. C.boils at low temperature
4. D.is colourless
Show answer
Answer: B. does not expand uniformily
AI explanation
Analyze the question: We're asked why water, though easily available, is not used as a thermometric liquid. A thermometric liquid must show a regular, uniform change in volume with temperature.
Explain the concept: A good thermometric liquid should:
Expand uniformly (linearly) with temperature
Be visible (opaque or colourable)
Not cling to glass (does not wet it)
Have a wide liquid range (low freezing point, high boiling point)
Have a fairly high expansivity and respond quickly to heat
Step-by-step evaluation:
A. Clings to glass: Water does cling to glass, which is a drawback, but it is not the main reason.
B. Does not expand uniformly: Water has an anomalous expansion. It contracts when heated from 0°C to 4°C, reaches maximum density at 4°C, and only then expands. Because its volume does not change regularly with temperature, it cannot give a reliable, evenly spaced scale. This is the fundamental reason.
C. Boils at low temperature: Water boils at 100°C, which is actually fairly high compared with alcohol. So this is incorrect.
D. Is colourless: Colourless liquids can be dyed (alcohol is coloured red), so this is a minor issue.
Answer: The main reason is that water does not expand uniformly (its anomalous expansion between 0°C and 4°C), which is option B.
Exam tip: Remember "4°C anomaly". Whenever a question asks why water is a poor thermometric liquid, think of its irregular expansion between 0°C and 4°C. Also remember that mercury is preferred because it expands uniformly, is opaque, and does not wet glass.
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23.
What are cathode rays?
1. A.Stream of electrons
2. B.Beam of neutrons
3. C.Beam of protons
4. D.Stream of alpha particles
Show answer
Answer: A. Stream of electrons
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24.
In which of the following states is MAXIMUM pressure exerted on a person
1. A.Standing on two feet
2. B.Standing on one foot
3. C.Lying on the floor
4. D.Kneeling on the floor
Show answer
Answer: B. Standing on one foot
AI explanation
Analyze the question: We want the position in which the person exerts the greatest pressure on the ground (the question says "exerted on a person", but it is clearly asking about the pressure the person exerts on the floor).
Concept: Pressure is force per unit area:
P = F / A
The force here is the person's weight (W = mg), which stays the same in every position. So pressure depends only on the contact area:
Smaller contact area → greater pressure
Larger contact area → smaller pressure
Solution: Compare the contact area in each position:
A. Standing on two feet: area = 2 foot areas
B. Standing on one foot: area = 1 foot area (smallest)
C. Lying on the floor: area = whole body (largest)
D. Kneeling: area = two knees plus lower legs (larger than one foot)
The weight is the same, so the smallest area gives the maximum pressure. That is standing on one foot.
For example, if a person weighs 600 N and one foot has area 0.02 m²:
On one foot: P = 600 / 0.02 = 30,000 Pa
On two feet: P = 600 / 0.04 = 15,000 Pa
Standing on one foot gives double the pressure of standing on two feet.
Answer: B. Standing on one foot.
Exam tip: For "maximum pressure" questions with the same force, look for the smallest area (think of high heels or a sharp knife). For "minimum pressure", look for the largest area (think of lying down on thin ice to spread your weight).
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25.
The depolarizing agent in a Leclanché cell is
1. A.powdered carbon.
2. B.manganese (IV) oxide.
3. C.carbon rod.
4. D.ammonium.
Show answer
Answer: B. manganese (IV) oxide.
AI explanation
Analyze the question: It asks which substance in a Leclanché cell removes the hydrogen bubbles that form at the positive electrode. That substance is called the depolarizing agent.
Concept: The Leclanché cell is a primary (non-rechargeable) cell. Its parts are:
Negative electrode: zinc case
Positive electrode: carbon rod
Electrolyte: ammonium chloride (NH₄Cl) paste or solution
Depolarizer: manganese (IV) oxide (MnO₂), also called manganese dioxide
Problem (polarization): As the cell works, hydrogen gas forms at the carbon rod. The bubbles coat the rod and insulate it. This raises the internal resistance and lowers the current, so the cell's output drops. This effect is called polarization.
Solution:
Manganese (IV) oxide is an oxidizing agent, so it reacts with the hydrogen before it can build up on the rod.
Reaction: 2MnO₂ + H₂ → Mn₂O₃ + H₂O
Checking the options: • A. Powdered carbon is mixed in to improve conductivity, but it does not remove hydrogen. • B. Manganese (IV) oxide oxidizes the hydrogen, so it is the depolarizer. • C. The carbon rod is the positive electrode (the collector). • D. Ammonium is part of the electrolyte (NH₄Cl), not the depolarizer.
Answer: B. Manganese (IV) oxide.
Tip: Remember "MnO₂ Mops up hydrogen." The depolarizer is always the chemical that gets rid of the hydrogen bubbles. In the Leclanché cell, carbon conducts, zinc is the negative terminal, NH₄Cl is the electrolyte, and MnO₂ is the depolarizer.
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26.
A stone of mass 200 g attached to a string is made to revolve in a horizontal circle of radius 1.5 m at a steady speed of 5 m/s. Calculate the tension in the string at the bottom of the circle.
1. A.5.3 N
2. B.3.3 N
3. C.2.0 N
4. D.1.3 N
Show answer
Answer: A. 5.3 N
AI explanation
Analyze the question: A 200 g stone moves in a circle of radius 1.5 m at 5 m/s. The question says "horizontal circle" but also asks for tension "at the bottom of the circle", which suggests a vertical circle. I'll work through both readings.
Concept: The net force toward the centre provides the centripetal force, F = mv²/r.
Data:
m = 0.2 kg
v = 5 m/s
r = 1.5 m
g = 10 m/s²
Centripetal force: F = mv²/r = (0.2 × 25)/1.5 = 5/1.5 ≈ 3.33 N
Reading 1: truly horizontal circle Tension alone supplies the centripetal force, so T ≈ 3.3 N (option B). This would be the same at every point on the circle. Strictly, a string can't stay perfectly horizontal while carrying the weight, so this reading is idealised.
Reading 2: vertical circle, at the bottom At the bottom, tension acts upward (toward the centre) and weight acts downward:
T − mg = mv²/r T = mv²/r + mg = 3.33 + (0.2 × 10) = 3.33 + 2.0 = 5.33 N ≈ 5.3 N
This matches option A.
Which one is right? The phrase "at the bottom of the circle" only makes sense if the weight matters, so the vertical-circle calculation is intended. That gives 5. The word "horizontal" in the question looks like a wording slip. If the circle really were horizontal, the answer would be 3.3 N, but then "at the bottom" would have no meaning.
Answer: T = 5.3 N, option A.
Exam tip: For vertical circles, remember:
Bottom: T = mv²/r + mg (tension is largest here)
Top: T = mv²/r − mg (tension is smallest here)
Check the position named in the question before choosing the formula.
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27.
To convert a milli-ammeter to an ammeter, a resistor of low value is necessary to connect a resistor of
1. A.low value in series with it
2. B.high value in series with it
3. C.low value in parallel with it
4. D.high value in parallel with it
Show answer
Answer: C. low value in parallel with it
AI explanation
Analyze the question: A milli-ammeter can only carry a small current through its coil. To make it measure larger currents (an ammeter), we must extend its range. The question is asking what kind of resistor to add, and how to connect it.
Concept: To extend the range of a galvanometer or milli-ammeter, we connect a shunt. A shunt is a resistor of very low resistance connected in parallel with the meter.
Why this works:
In a parallel connection, current divides between the branches. The branch with the lower resistance takes the larger share of the current.
The low-resistance shunt carries most of the current, so only a small, safe fraction passes through the milli-ammeter coil.
The total current the combination can measure is therefore much larger.
The combined resistance of the meter and shunt is also very small, so the ammeter has little effect on the circuit it is placed in. This is what an ideal ammeter should have.
Shunt formula:
R_s = I_g R_g / (I − I_g)
where I_g is the full-scale current of the milli-ammeter, R_g is its resistance, and I is the new maximum current. Since I is much larger than I_g, R_s comes out very small.
Checking the options:
A. Low value in series: this adds resistance in line with the meter and does not divert any current. Wrong.
B. High value in series: this is used to make a voltmeter (a multiplier). Wrong.
C. Low value in parallel: this is a shunt. Correct.
D. High value in parallel: almost all the current would still go through the meter and damage it. Wrong.
Answer: C. low value in parallel with it
Exam tip: Remember it as follows:
Ammeter = Amall (small) resistance in parallel (shunt)
Voltmeter = Very large resistance in series (multiplier)
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28.
Four pieces of constantan wire, marked E, F, G, and H, each of length 1.0m, are at the temperature. Their respective diameters are 1 mm, 2 mm, 6 mm, and 10 mm. Which wire has the highest resistance?
1. A.E
2. B.F
3. C.G
4. D.H
Show answer
Answer: A. E
AI explanation
Analyze the question: Four wires of the same material (constantan), same length (1.0 m) and same temperature differ only in diameter. We need the one with the highest resistance. Concept: Resistance of a wire is R = ρL / A where ρ is resistivity (same for all, since the material and temperature are the same), L is length (same for all), and A is cross-sectional area. So R ∝ 1/A. Since A = πd²/4, we get R ∝ 1/d². The thinner the wire, the higher the resistance. Solution: Compare the quantity 1/d² for each wire. | Wire | Diameter (mm) | 1/d² (relative) | |------|---------------|-----------------| | E | 1 | 1 | | F | 2 | 1/4 = 0.25 | | G | 6 | 1/36 ≈ 0.028 | | H | 10 | 1/100 = 0.01 | Wire E has the largest value of 1/d², so it has the highest resistance. Wire H has the lowest. Answer: A. E Tip: For wires of the same material, length and temperature, remember "thin wire, high resistance." Resistance is inversely proportional to the square of the diameter. Wire E is the thinnest, so it resists current flow the most, just as a narrow pipe resists water flow more than a wide one.
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29.
Which of the following modes is the most economical method of transmitting electrical power over a long distance?
1. A.Alternating current at high voltage and low current.
2. B.Alternating current at low voltage and high current.
3. C.Direct current at high voltage and low current.
4. D.Direct current at low voltage and high current.
Show answer
Answer: A. Alternating current at high voltage and low current.
AI explanation
Analyze the question: We want to send power over a long distance while wasting as little energy as possible, and at a practical cost.
Concept:
Power transmitted: P = IV
Power lost in the cables: P_loss = I²R
For a fixed power P, raising the voltage V lowers the current I (since I = P/V). Because the loss depends on I², even a small drop in current cuts the loss sharply.
Step by step:
Low current means a small I²R loss, so less energy is wasted as heat in the cables.
High voltage is therefore needed to deliver the same power with low current.
Alternating current or direct current? AC can be stepped up and stepped down easily and cheaply using transformers. This is how the National Grid in Nigeria works: power is stepped up to 330 kV or 132 kV for transmission, then stepped down for homes. Transformers do not work with DC, and converting DC voltages needs costly equipment, so DC is less economical for general use.
Eliminating the options:
B: High current causes large I²R losses. ✗
C: DC at high voltage works in special cases, but it cannot be easily transformed, so it is not the standard economical method. ✗
D: DC at high current has large losses. ✗
A: AC at high voltage and low current has low losses and easy transformation. ✓
Answer: A
Tip: Remember "HV–LC–AC": High Voltage, Low Current, Alternating Current is the combination for transmission. Whenever you see the words "economical" and "long distance," think of the I²R loss and transformers.
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30.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.
31.
The vacuum and silvered wall surfaces of a vacuum flask walls are respectively
1. A.minimize conduction and convection and prevent radiation
2. B.prevent conduction and convection and minimize radiation
3. C.prevent conduction and minimize convection and radiation
4. D.minimize convection and prevent conduction and radiation
Show answer
Answer: B. prevent conduction and convection and minimize radiation
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32.
A boy of mass 40 kg jumps off a stationary skateboard and moves horizontally with a speed of 1.5 m/s while the skateboard moves in the opposite direction with a speed of 20 m/s. Calculate the mass of the skateboard.
1. A.60 kg
2. B.40 kg
3. C.3 kg
4. D.2 kg
Show answer
Answer: C. 3 kg
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33.
A body of mass, m is projected vertically upward with a velocity, y. At what position will the potential energy be maximum?
1. A. $\frac{y}{g}$
2. B. $\frac{2y^2}{g}$
3. C. $\frac{y^2}{2g}$
4. D. $\frac{y^2}{4g}$
Show answer
Answer: C. $\frac{y^2}{2g}$
AI explanation
Analyze the question: A body is thrown straight up with speed "y" (the question uses y for the initial velocity). Potential energy is greatest at the highest point, where the body momentarily stops. We need that height.
Concept: At maximum height, all the kinetic energy has changed into potential energy (conservation of energy). Equivalently, we can use the equation of motion v² = u² − 2gh.
Solution:
Using energy conservation:
Initial kinetic energy = ½my²
Potential energy at maximum height h = mgh
Set them equal:
½my² = mgh
Cancel m:
h = y²/(2g)
Check with the equation of motion: at the top, final velocity v = 0, so 0 = y² − 2gh, which gives h = y²/(2g).
The potential energy is maximum at a height of y²/(2g).
Answer: Option C
Tip: "Maximum height" in vertical projection is always u²/(2g). Remember that at the top the velocity is zero, so v² = u² − 2gh quickly gives the height. Also notice that the mass cancels out, so the height does not depend on m. Option A (y/g) is the time to reach the top, which is a common distractor.
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34.
A non-conducting vessel contains a liquid of mass 70 g at 25º C. Another 70.0g of the same liquid at 35ºC is quickly poured into the vessel. Determine the final temperature of the mixture
1. A.15ºC
2. B.20ºC
3. C.30ºC
4. D.40ºC
Show answer
Answer: C. 30ºC
AI explanation
Analyze the question
Two equal masses of the same liquid at different temperatures are mixed in a non-conducting (insulated) vessel. We want the final equilibrium temperature.
Concept
With no heat lost to the surroundings (and the vessel absorbing no heat), the principle of conservation of heat energy applies:
Heat lost by the hot liquid = Heat gained by the cold liquid
Heat is given by Q = mcΔθ, where m is mass, c is specific heat capacity, and Δθ is the temperature change.
Solution
Let the final temperature be θ.
Cold liquid gains heat: Q₁ = 70 × c × (θ − 25)
Hot liquid loses heat: Q₂ = 70 × c × (35 − θ)
Setting Q₁ = Q₂:
70c(θ − 25) = 70c(35 − θ)
The 70c cancels on both sides:
θ − 25 = 35 − θ 2θ = 60 θ = 30 °C
This agrees with the mean of the two temperatures: (25 + 35)/2 = 30 °C. That is expected, because the masses and the liquid are the same.
Answer: C. 30 °C.
Tip
When equal masses of the same substance are mixed, the final temperature is simply the average of the two starting temperatures. You can skip the long working and save time in the exam. If the masses are different, use the full equation: θ = (m₁θ₁ + m₂θ₂)/(m₁ + m₂).
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35.
The phenomenon used for explaining the formation of a rainbow in the sky is
1. A.interference.
2. B.refraction.
3. C.reflection.
4. D.dispersion.
Show answer
Answer: D. dispersion.
AI explanation
Analyze the question: It asks for the phenomenon that explains how a rainbow forms. Several processes are involved, but we need the one that explains the colours appearing in the sky.
Concept: A rainbow forms when sunlight (white light) enters raindrops, and three things happen:
Refraction: light bends as it enters the water droplet.
Dispersion: white light splits into its component colours (red, orange, yellow, green, blue, indigo, violet). This happens because each colour has a different wavelength and therefore a different refractive index in water. Violet bends the most and red the least.
Internal reflection: the light reflects off the back of the droplet.
Refraction again: the light bends once more as it leaves the droplet, and the separated colours reach the observer's eye.
Solution:
Interference (A) involves the superposition of waves, as in thin soap films. It is not the main cause of a rainbow.
Refraction (B) is part of the process, but refraction alone only bends the light. It does not explain why the colours separate.
Reflection (C) occurs inside the droplet, but it does not separate colours.
Dispersion (D) is the splitting of white light into its spectrum of colours. This is what gives a rainbow its band of colours.
Answer: D. dispersion
Tip: Think "rainbow = colours separated = dispersion." If a question asks about the separation of white light into colours (rainbow, prism), the answer is dispersion. If it asks about the bending of light as it changes medium, the answer is refraction.
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36.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.
37.
The correct sequence of ionization power of alpha particle, gamma ray, and beta particle respectively is
1. A.low, medium, high.
2. B.high, medium, low.
3. C.medium, low, high.
4. D.high, low, medium.
Show answer
Answer: D. high, low, medium.
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38.
Which of the following terms has different dimension from the others?
1. A.Stress x Strain
2. B.Pressure
3. C. $\frac{\text{stress}}{\text{strain}}$
4. D.Torque
Show answer
Answer: D. Torque
AI explanation
Analyze the question: We need to find the quantity whose dimension differs from the rest. So we find the dimensions of each option.
Key concepts:
Stress = Force/Area, so its dimension is MLT⁻² / L² = ML⁻¹T⁻²
Strain = change in length/original length, so it is dimensionless
Pressure = Force/Area, so its dimension is ML⁻¹T⁻²
Torque = Force × perpendicular distance, so its dimension is MLT⁻² × L = ML²T⁻²
Step by step:
A. Stress × Strain = ML⁻¹T⁻² × 1 = ML⁻¹T⁻²
B. Pressure = ML⁻¹T⁻²
C. Stress/Strain (this is Young's modulus) = ML⁻¹T⁻² ÷ 1 = ML⁻¹T⁻²
D. Torque = ML²T⁻²
Options A, B and C all have the dimension ML⁻¹T⁻². Only torque (D) has ML²T⁻², which is the same as the dimension of energy or work.
Answer: D
Tip: Strain is dimensionless, so multiplying or dividing by it never changes the dimension. Also remember that pressure, stress and Young's modulus all share ML⁻¹T⁻², while torque and energy share ML²T⁻². Torque and work have the same dimension even though they are different physical quantities.
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39.
The magnitude of the acceleration of a moving object is equal to the
1. A.gradient of a displacement-time graph
2. B.gradient of a velocity-time graph
3. C.area below a force-time graph
4. D.area below a velocity-time graph
Show answer
Answer: B. gradient of a velocity-time graph
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40.
A 2 μF capacitor is connected directly across a 150 V $_{rms}$ , 60 Hz A.C source. Calculate the r m s value of the current.
1. A.0.113 A
2. B.0.160 A
3. C.150 A
4. D.1324 A
Show answer
Answer: A. 0.113 A
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41.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.
42.
A ray of light travels from a less dense medium to a denser medium. How are the speed and frequency of the light affected? The speed
1. A.Increases and the frequency increases
2. B.decreases and the frequency decreases
3. C.increases and the frequency remains the same
4. D.decreases and the frequency remains the same
Show answer
Answer: D. decreases and the frequency remains the same
AI explanation
Analyze the question: Light moves from a less dense (e.g. air) medium into a denser (e.g. glass or water) medium. We need to say what happens to its speed and its frequency.
Concept:
Speed of light in a medium is v = c/n, where n is the refractive index. A denser medium has a higher n, so the speed decreases.
Frequency is fixed by the source of the light. It does not change when light crosses a boundary, because the number of waves arriving at the boundary per second must equal the number leaving it per second. So the frequency remains the same.
Since v = fλ and f is constant, a decrease in v means the wavelength λ also decreases. This is why light bends towards the normal when entering a denser medium.
Step-by-step solution:
Moving into a denser medium means n increases.
v = c/n, so v decreases.
The frequency is determined by the source, so f stays constant.
Wavelength decreases (λ = v/f).
Checking the options:
A: Speed increases and frequency increases. Wrong on both.
B: Speed decreases, which is right, but frequency does not decrease. Wrong.
C: Speed does not increase. Wrong.
D: Speed decreases and frequency remains the same. Correct.
Tip: When a wave crosses a boundary, remember "F is fixed". Speed and wavelength change together, but frequency never does. Going into a denser medium makes light slower, with a shorter wavelength and the same frequency.
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43.
The inside portion of a hollow metal sphere of diameter 20 cm is polished. The portion will therefore form a
1. A.Concave mirror of focal length 5cm.
2. B.Concave mirror of focal length 10 cm.
3. C.Convex mirror of focal length 10 cm
4. D.Convex mirror of focal length 5cm
Show answer
Answer: A. Concave mirror of focal length 5cm.
AI explanation
Analyze the question: A hollow sphere has a diameter of 20 cm, so its radius is 10 cm. The inside surface is polished, so light reflects from the inner, curved-inward surface.
Concept:
A spherical mirror whose reflecting surface curves inward (like the inside of a bowl) is a concave mirror.
The radius of curvature (R) of the mirror equals the radius of the sphere.
The focal length is half the radius of curvature: f = R/2
Solution:
Diameter = 20 cm, so radius R = 20 ÷ 2 = 10 cm.
The inside is polished, so it forms a concave mirror.
f = R/2 = 10/2 = 5 cm.
So the polished inner portion is a concave mirror of focal length 5 cm.
Checking the options:
A. Concave, 5 cm ✔
B. Concave, 10 cm ✘ (this mistakes the radius for the focal length)
C and D. Convex ✘ (a convex mirror would need the outside surface polished)
Tip: Remember "Inside = Cave": the inside of a sphere gives a concave mirror. Always use f = R/2, and don't confuse the diameter, radius, and focal length. Diameter → halve it to get R → halve again to get f. So f = diameter/4 here: 20/4 = 5 cm.
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44.
Chromatic aberration in lenses can be corrected by using a combination of
1. A.diverging and converging lenses.
2. B.an opaque material to cover the rims of lenses.
3. C.wide parallel beams on the lenses' surface.
4. D.a thin convex lens.
Show answer
Answer: A. diverging and converging lenses.
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45.
The maximum displacement of particles from equilibrium position in a wave motion is known as
1. A.wave length.
2. B.amplitude.
3. C.frequency.
4. D.polarization.
Show answer
Answer: B. amplitude.
AI explanation
Step 1: Analyze the question The question asks for the name given to the maximum displacement of a vibrating particle from its rest (equilibrium) position as a wave passes.
Step 2: Explain the concept When a wave travels through a medium, the particles of the medium oscillate about their rest positions. The key terms are:
Wavelength (λ): the distance between two successive points in phase, such as crest to crest. It is a distance along the direction of travel, not a displacement of particles.
Amplitude (A): the maximum displacement of a particle from its equilibrium position. It is a measure of the wave's energy, since energy is proportional to A².
Frequency (f): the number of complete oscillations per second, measured in hertz (Hz).
Polarization: the restriction of a transverse wave's vibrations to one plane. It is a property of the wave's direction of vibration, not a size of displacement.
Step 3: Match the definition to the options
A. Wavelength is a length of one complete wave, so it does not match.
B. Amplitude is the maximum displacement from equilibrium, so it matches.
C. Frequency is a rate (cycles per second), so it does not match.
D. Polarization concerns the plane of vibration, so it does not match.
Step 4: Answer The maximum displacement of particles from the equilibrium position in a wave motion is the amplitude, which is option B.
Exam tip: Think "A for Amplitude = Altitude of the crest". Amplitude is measured from the middle (rest) line up to the crest, or down to the trough. It is not the full crest-to-trough height, which is twice the amplitude.
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46.
A galvanometer of full-scale deflection 10 mA has a resistance of 5 $\Omega$ . Calculate the shunt needed to convert it to measure currents of 2 A.
1. A.0.025 $\Omega$
2. B.0.050 $\Omega$
3. C.0.250 $\Omega$
4. D.0.500 $\Omega$
Show answer
Answer: A. 0.025 $\Omega$
AI explanation
Analyze the question
A galvanometer only handles a small current (10 mA). To measure 2 A, we connect a low-resistance shunt in parallel with it so that the extra current bypasses the coil.
Concept
In parallel, both branches have the same voltage:
I_g × R_g = I_s × R_s
where I_s = I − I_g
Solution
Full-scale current: I_g = 10 mA = 0.010 A
Galvanometer resistance: R_g = 5 Ω
Total current wanted: I = 2 A
Shunt current: I_s = 2 − 0.010 = 1.99 A
R_s = (I_g × R_g) / I_s = (0.010 × 5) / 1.99 = 0.05 / 1.99 ≈ 0.0251 Ω
So R_s ≈ 0.025 Ω.
Answer
The shunt needed is about 0.025 Ω, which is option A.
Tip
Quick approximation: since 2 A is much larger than 10 mA, nearly all the current goes through the shunt, so R_s ≈ (0.01 × 5)/2 = 0.025 Ω. Remember the shunt is always parallel and very small, while a multiplier for a voltmeter is series and large.
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47.
The main difference between X-rays and gamma rays is in their
1. A.ionizing ability.
2. B.absorbing rate.
3. C.mode of propagation.
4. D.mode of production.
Show answer
Answer: D. mode of production.
AI explanation
Step 1: Analyze the question We are asked what really separates X-rays from gamma rays. Both are electromagnetic waves, so we need to find the one property that is truly different.
Step 2: Explain the concept
X-rays are produced when fast-moving electrons hit a heavy metal target (such as tungsten) and are decelerated, or when electrons in the inner shells of atoms change energy levels. The source is the electron cloud/orbitals outside the nucleus.
Gamma rays are produced by the nucleus of a radioactive atom when it de-excites after alpha or beta decay.
Both are high-frequency electromagnetic waves. They travel at the speed of light in a vacuum (3 × 10⁸ m/s), need no medium, and are not deflected by electric or magnetic fields.
Step 3: Check each option
A. Ionizing ability: Not a fundamental difference. It depends on photon energy, and X-rays and gamma rays have overlapping energy ranges.
B. Absorbing rate: Also depends on energy, not on what kind of ray it is.
C. Mode of propagation: Both are electromagnetic waves travelling in straight lines at the speed of light, so they are the same.
D. Mode of production: X-rays come from electron transitions or electron deceleration, while gamma rays come from nuclear de-excitation. This is the true difference.
Step 4: Answer The correct option is D, mode of production.
Tip: Remember "X-rays = Extra-nuclear (electrons); Gamma = nucleus." In exams, when asked for the difference between two parts of the electromagnetic spectrum, look for origin/production or wavelength/frequency. Their propagation is always the same.
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48.
A body moves with uniform velocity when the resultant force on it is
1. A.greater than the frictional force acting on it
2. B.less than the frictional force acting on it
3. C.equal to zero
4. D.equal to unity
Show answer
Answer: C. equal to zero
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49.
In which of the following devices is the thermal expansion considered a disadvantage?
1. A.Fire alarm
2. B.Thermostat
3. C.Bimetallic thermometer
4. D.Balance wheel of a watch
Show answer
Answer: D. Balance wheel of a watch
AI explanation
Analyze the question: We need the device where thermal expansion is a disadvantage (an unwanted effect), not one that deliberately uses expansion to work.
Concept: Thermal expansion is the increase in size of a material when heated. Many devices use it on purpose:
Fire alarm: A bimetallic strip bends when heated and completes a circuit to ring the bell. Expansion is useful.
Thermostat: A bimetallic strip bends to switch a heating or cooling circuit on or off. Expansion is useful.
Bimetallic thermometer: The strip coils or bends in proportion to temperature, which moves the pointer. Expansion is useful.
Balance wheel of a watch: The balance wheel controls the timing of the watch. If it expands when it gets warm, its size changes, which changes its moment of inertia and therefore its oscillation period. The watch then gains or loses time. Expansion here is harmful, so the wheel is made from special alloys (such as invar-type compensating balances) to reduce it.
Solution:
Devices A, B and C depend on expansion to function.
The balance wheel needs a constant size to keep accurate time, so any expansion causes timing errors.
Therefore thermal expansion is a disadvantage in the balance wheel of a watch.
Tip: Ask yourself, "Does the device use expansion to work?" Bimetallic strips (alarms, thermostats, thermometers) use it. Precision timekeepers and measuring instruments (watch balance wheels, pendulum clocks, steel tapes) need it avoided, which is why invar is used.
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50.
The constant temperature at which a liquid change into gaseous state is known as
1. A.evaporation point
2. B.boiling point
3. C.melting point
4. D.dew point
Show answer
Answer: B. boiling point
AI explanation
Step 1: Analyze the question The question asks for the name of the constant temperature at which a liquid changes into a gas.
Step 2: Explain the concept When a liquid is heated, its temperature rises until it reaches a certain value. At that temperature, bubbles of vapour form throughout the liquid, and it changes to a gas. While this change happens, the temperature stays constant, because the heat supplied goes into breaking the bonds between molecules (latent heat of vaporization) rather than raising the temperature. This temperature is called the boiling point.
Step 3: Check each option
A. Evaporation point: Not a standard physics term. Evaporation occurs at any temperature, only at the surface, so there is no fixed "evaporation point."
B. Boiling point: The fixed temperature at which a liquid changes to gas throughout its body. For pure water at standard atmospheric pressure it is 100°C.
C. Melting point: The temperature at which a solid changes to a liquid.
D. Dew point: The temperature at which air becomes saturated and water vapour condenses into liquid droplets (the reverse direction, gas to liquid).
Step 4: Answer The correct answer is B. boiling point.
Tip: Remember the direction of each change:
Melting point: solid → liquid
Boiling point: liquid → gas
Dew point: gas → liquid (condensation)
Also remember that boiling happens at a constant temperature and throughout the liquid, while evaporation happens at any temperature and only at the surface.
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