Explanation:

The correct answer is: B

In a mass spectrometer, the ion moves in a circular path due to the magnetic force. The magnetic force \( q v B \) provides the centripetal force \( \frac{m v^2}{r} \). Setting them equal:

\[ \begin{aligned} q v B &= \frac{m v^2}{r} \\[1em] q B &= \frac{m v}{r} \quad (\text{divide by } v) \\[1em] v &= \frac{q B r}{m} \end{aligned} \]

This matches option B, \( \frac{B q r}{m} \).

Explanation:

The correct answer is: A

The wavelength \( \lambda \) is calculated using \( v = f \lambda \), where \( v = 331 \, \text{m} \, \text{s}^{-1} \) (speed) and \( f = 512 \, \text{s}^{-1} \) (frequency in Hz). Solving for \( \lambda \):

\[ \begin{aligned} \lambda &= \frac{v}{f} \\[1em] &= \frac{331}{512} \\[1em] &\approx 0.646 \, \text{m} \end{aligned} \]

Units check: \( \frac{\text{m} \, \text{s}^{-1}}{\text{s}^{-1}} = \text{m} \), which is correct for wavelength. Thus, the wavelength is 0.646 m.

Explanation:

The correct answer is: A

Only a few alpha particles were deflected because the nucleus is very small and carries a positive charge. Most particles passed straight through the gold foil, showing that atoms are mostly empty space.

Here's why the other answers are incorrect:

• B: The nucleus does not emit alpha particles in this experiment.


• C: The nucleus does not contain alpha particles; alpha particles are just used as the probe.


• D: Electrons are not found inside the nucleus — only protons (and neutrons).

Explanation:

The correct answer is: C

The work done \( W \) is calculated using the formula \( W = Q \cdot V \), where \( Q = 10 \, \text{C} \) (charge) and \( V = 220 \, \text{V} \) (potential difference):

\[ \begin{aligned} W &= Q \cdot V \\[1em] &= 10 \cdot 220 \\[1em] &= 2200 \, \text{J} \end{aligned} \]

Thus, the work done is 2200 J.

Explanation:

The correct answer is: A. Brass rod

The magnetic field of a solenoid becomes stronger when a magnetic (ferromagnetic) material is inserted inside it. Metals like soft iron, steel, and nickel increase the magnetic field.

Brass is **non-magnetic**, so inserting it will not increase the magnetic field.

Here's why the other answers are incorrect:

• B. Soft iron: Strongly magnetic — greatly increases the field.


• C. Steel: Magnetic — increases the field.


• D. Nickel: Magnetic — increases the field.

Explanation:

The correct answer is: C

A dielectric is an **insulator**, so it prevents current from flowing across the plates. It increases capacitance and allows the capacitor to hold more charge safely.

Here's why the other answers are incorrect:

• A: A dielectric increases the maximum voltage the capacitor can handle.


• B: A dielectric increases capacitance.


• D: It physically keeps the plates separated.

Explanation:

The correct answer is: B. It has a high susceptibility

Ferromagnetic materials (like iron and nickel) are strongly attracted to magnets because they can become highly magnetized. This is due to their high magnetic susceptibility.

Here's why the other answers are incorrect:

• A: Ferromagnets have high permeability, not low.


• C: They attract magnetic materials — they do not repel them.


• D: They do not attract non-magnetic materials.

Explanation:

The correct answer is: A

Both balls experience the same acceleration due to gravity (g). Gravity always acts downward, regardless of whether the ball is moving up or down.

Here's why the other answers are incorrect:

• B: The accelerations are not opposite — both are downward.


• C: Neither ball has less acceleration — gravity is the same for both.


• D: Gravity is constant, so the accelerations cannot be different.

Explanation:

The correct answer is: C

The escape velocity is the minimum speed required for an object to escape a planet’s gravitational pull, reaching infinity with zero kinetic energy. Using conservation of energy, the kinetic energy at the surface, \( \frac{1}{2} m v^2 \), equals the gravitational potential energy, \( \frac{G M m}{R} \). Setting them equal:

\[ \begin{aligned} \frac{1}{2} m v^2 &= \frac{G M m}{R} \\[1em] \frac{1}{2} v^2 &= \frac{G M}{R} \quad (\text{divide by } m) \\[1em] v^2 &= \frac{2 G M}{R} \\[1em] v &= \left( \frac{2 G M}{R} \right)^{1/2} \end{aligned} \]

This matches option C, \( \left( \frac{2 G M}{R} \right)^{1/2} \).

Explanation:

The correct answer is: D

The specific latent heat of vaporization is the amount of thermal energy required to change 1 kg of a substance from liquid (molten) to vapor phase at constant temperature and pressure.

Here, the value \( 8.7 \times 10^5 \, \mathrm{J \, kg^{-1}} \) means:

\[ \text{Energy required} = 8.7 \times 10^5 \, \mathrm{J} \] to change \[ 1\, \mathrm{kg} \] of molten lead to vapour at constant temperature and pressure.

It does not apply to the solid phase directly, nor does it depend on temperature change during the phase transition.

Therefore, the correct answer is D.

Explanation:

The correct answer is: B

The forces opposing the motion are the component of the weight down the incline and the frictional force.

Given:

Mass, \( m = 100\, \mathrm{kg} \)
Incline angle, \( \theta = 30^\circ \)
Coefficient of friction, \( \mu = 0.25 \)
Gravity, \( g = 10\, \mathrm{m/s}^2 \)

Weight component down the incline:

\[ W_{\parallel} = mg \sin \theta \] \[ = 100 \times 10 \times \sin 30^\circ \] \[ = 1000 \times 0.5 \] \[ = 500\, \mathrm{N} \]

Normal force:

\[ N = mg \cos \theta \] \[ = 100 \times 10 \times \cos 30^\circ \] \[ = 1000 \times 0.866 \] \[ = 866\, \mathrm{N} \]

Frictional force:

\[ f = \mu N \] \[ = 0.25 \times 866 \] \[ = 216.5\, \mathrm{N} \]

Total opposing force is sum of weight component and friction:

\[ F_{\text{opposing}} = W_{\parallel} + f \] \[ = 500 + 216.5 \] \[ = \boxed{716.5\, \mathrm{N}} \]

Thus, the correct answer is B. 716.5 N.

Explanation:

The correct answer is: D

Both objects start from rest, with object A having acceleration \( a \) and object B having acceleration \( 2a \). Assuming they accelerate for the same time \( t \), the distance traveled is given by:

\[ s = \frac{1}{2} a t^2 \]

For object A:

\[ s_A = \frac{1}{2} a t^2 \]

For object B:

\[ \begin{aligned} s_B &= \frac{1}{2} (2a) t^2 \\ &= a t^2 \end{aligned} \]

The ratio of distances is:

\[ \begin{aligned} \frac{s_B}{s_A} &= \frac{a t^2}{\frac{1}{2} a t^2} \\ &= 2 \end{aligned} \]

Thus, B travels twice as far as A, matching option D.

Explanation:

The correct answer is: D. E

Hot air rises. The hot metal warms the air around it, and this warm air moves upward to the top of the box, making the thermometer at the top (E) record the highest temperature.

Here's why the other answers are incorrect:

• F and H: On the sides, so they measure medium temperature.


• G: At the bottom — cold air sinks, so it records the lowest temperature.

Explanation:

The correct answer is: A

During evaporation, the most energetic molecules escape from the surface of the liquid into the air. This reduces the amount of liquid left in the dish.

Here's why the other answers are incorrect:

• B: Least energetic molecules cannot escape the surface.


• C: Least energetic molecules do not escape — they stay in the liquid.


• D: Most energetic molecules do not return — they escape into the air.

Explanation:

The correct answer is: C. Violet and red

In visible light:

• Violet has the shortest wavelength.
• Red has the longest wavelength.

Here's why the other answers are incorrect:

• A: Yellow and blue are not at the wavelength extremes.


• B: Indigo does not have the shortest wavelength.


• D: Red is longest, but blue is not the shortest.

Explanation:

The correct answer is: A

Topic: Mirror Formula and Optics

The standard mirror and lens formulas include:

\[ \frac{1}{f} = \frac{1}{u} + \frac{1}{v} \]

\[ m = \frac{v}{u} \quad \text{and} \quad f = \frac{1}{D} \quad \ \]

However, the formula \[ N = \frac{360}{\theta} = -1 \] is not related to mirror equations and does not make physical or mathematical sense in this context.

Hence, option A is not a valid mirror formula.

Explanation:

The correct answer is: C

An atom becomes excited when it absorbs energy and one or more electrons jump to a higher energy level than normal.

Here's why the other answers are incorrect:

• A: The excited state refers to electrons moving, not potential energy alone.


• B: The conduction band refers to solids, not atoms.


• D: Minimum energy means ground state, not excited.

Explanation:

The correct answer is: D

A magnet, when freely suspended, always aligns itself in the Earth's magnetic field, pointing North–South. This proves the bar is magnetized.

Here's why the other answers are incorrect:

• A: A magnet aligns N–S, not E–W.


• B: Repulsion is rare and depends on pole orientation.


• C: Attraction is not conclusive — even unmagnetized magnetic materials can be attracted.

Explanation:

The correct answer is: C

A gold leaf electroscope shows how much charge is present because the gold leaves diverge. The more they spread, the greater the charge on the object.

Here's why the other answers are incorrect:

• A: An ebonite rod only becomes charged by rubbing — it does not measure charge.


• B: A proof plane is only used to transfer charge.


• D: An electrophorus produces charge, not measure it.

Explanation:

The correct answer is: C

The dielectric between capacitor plates is an insulator, so direct current cannot cross from one plate to the other.

Here's why the other answers are incorrect:

• A: Capacitor plates having opposite charges does not stop DC flow — the dielectric does.


• B: Leakage of charge is not the reason DC stops flowing.


• D: The plates are conducting — it's the dielectric that blocks current.

Explanation:

The correct answer is: B

Electromagnetic induction is the production of current when the magnetic field around a conductor changes.

Here's why the other answers are incorrect:

• A: Not a standard term in electricity.


• C: Electrostatic induction deals with charges, not current.


• D: Flux linkage is related, but it is not the name of the process.

Explanation:

The correct answer is: B

When heated, metal wires expand and become longer, causing them to sag.

Here's why the other answers are incorrect:

• A: Radiation does not stretch the wires — it's heat expansion.


• C: Gravity acts on the wires, but thermal expansion is the real cause of sagging.


• D: Handling wires does not cause permanent sagging.

Explanation:

The correct answer is: B

Topic: Electrical Circuits – EMF and Internal Resistance

Using Ohm’s law and the formula for EMF:

\[ \text{EMF} = I(R + r) \]

Where:

• \( \text{EMF} = 2 \ \text{V} \)
• \( I = 0.4 \ \text{A} \)
• \( r = 0.5 \ \Omega \) (internal resistance)
• \( R = \text{resistance of P} \)

Substitute into the equation:

\[ 2 = 0.4(R + 0.5) \]

Divide both sides by 0.4:

\[ \frac{2}{0.4} = R + 0.5 \]

\[ 5 = R + 0.5 \]

\[ R = 5 - 0.5 = 4.0 \ \Omega \]

Therefore, the resistance of P is 4.0 Ω.

Explanation:

The correct answer is: B

Heat always flows from a body at a higher temperature to one at a lower temperature.

Here's why the other answers are incorrect:

• A: Heat capacity is how much heat is needed to change a body’s temperature — it does not set heat flow direction.


• C: Mass does not determine heat flow direction.


• D: Power is the rate of doing work — unrelated to heat flow direction.

Explanation:

The correct answer is: A

Topic: RLC Series Circuits and Resonance

At resonance in an RLC series circuit, the inductive reactance \( X_L \) is equal to the capacitive reactance \( X_C \).

Thus, the voltage across the inductor \( V_L \) and the voltage across the capacitor \( V_C \) are equal in magnitude but opposite in direction:

\[ V_L = -V_C \]

Given:

\[ V_L = 40 \text{ V} \Rightarrow V_C = 40 \text{ V} \]

So, the voltage across the capacitor is 40 V.

Explanation:

The correct answer is: A

The commutator reverses the direction of current in the coil every half turn so that the torque keeps acting in the same direction, allowing continuous rotation.

Here's why the other answers are incorrect:

• B: A uniform couple results from the current reversal, but this is not the function of the commutator — it's a consequence.


• C: Speed of rotation depends on supply voltage and load, not the commutator.


• D: The commutator does not increase efficiency; it only maintains the direction of rotation.

Explanation:

The correct answer is: D

Topic: Conservation of Momentum and Kinetic Energy

Given:

\( m_1 = 0.05\, \text{kg}, \quad v_1 = 200\, \text{m s}^{-1} \)
\( m_2 = 0.95\, \text{kg}, \quad v_2 = 0\, \text{m s}^{-1} \)

Assuming the bullet embeds in the block (perfectly inelastic collision), they move together at speed \( v \).

By conservation of momentum:

\[ m_1 v_1 + m_2 v_2 = (m_1 + m_2) v \]

Substituting values:

\[ \begin{aligned} (0.05)(200) + (0.95)(0) &= (0.05 + 0.95) v \\ 10 &= 1.0 \times v \\ v &= 10\, \text{m s}^{-1} \end{aligned} \]

Kinetic energy of block after impact:

\[ \begin{aligned} KE &= \frac{1}{2} m_2 v^2 \\ &= \frac{1}{2} \times 0.95 \times (10)^2 \\ &= 0.475 \times 100 \\ &= 47.5\, \text{J} \approx 50\, \text{J} \end{aligned} \]

Therefore, the kinetic energy is approximately 50 J.

Explanation:

The correct answer is: A

The nuclear force is the strong force that holds protons and neutrons together inside the nucleus. It is extremely powerful and overcomes the electrostatic repulsion between the positively charged protons.

Here's why the other answers are incorrect:

• B. Electrostatic force: This causes repulsion between protons, not attraction.


• C. Magnetic force: Related to moving charges or magnets, not nucleon attraction.


• D. Gravitational force: Too weak at the atomic scale to hold nucleons together.

Explanation:

The correct answer is: C

Control rods absorb neutrons to regulate the chain reaction inside the reactor. By absorbing neutrons, they control how many further fissions occur and thus regulate the energy released.

Here's why the other answers are incorrect:

• A: Control rods directly affect neutron production by absorbing neutrons.


• B: Changing neutron absorption changes the rate of fission, altering energy output.


• D: Neutron speed is controlled by moderators, not control rods.

Explanation:

The correct answer is: B

Topic: Electrical Power and Safety

Step 1: Convert the power rating from kilowatts to watts.

\[ P = 1.06\,\text{kW} = 1060\,\text{W} \]

Step 2: Use the formula \( I = \frac{P}{V} \) to calculate the current.

\[ I = \frac{1060}{220} \approx 4.82\,\text{A} \]

Step 3: Choose a fuse slightly above the calculated current.

So, the appropriate fuse rating is 5 A.

Explanation:

The correct answer is: A

A concave mirror produces a magnified and upright image when the object is close to it. Dentists use concave mirrors so that the teeth appear larger and clearer.

Here's why the other answers are incorrect:

• B. Plane mirror: Forms an image of the same size — no magnification.


• C. Cylindrical mirror: Distorts the image; not suitable for inspection.


• D. Convex mirror: Produces diminished images — used for wide views, not magnification.

Explanation:

The correct answer is: A

The diagram shows a standing wave with 5 loops, indicating the fifth harmonic (\( n = 5 \)). For a wire fixed at both ends, \( \lambda = \frac{2L}{n} \), where \( L = 1.25 \, \text{m} \):

\[ \begin{aligned} \lambda &= \frac{2 \times 1.25}{5} \\[1em] &= 0.50 \, \text{m} \end{aligned} \]

Thus, the wavelength is 0.50 m.

Explanation:

The correct answer is: B

Using the wavelength \( \lambda = 0.50 \, \text{m} \) from Question 39 and the wave speed \( v = 120 \, \text{m/s} \), the frequency is:

\[ \begin{aligned} f &= \frac{v}{\lambda} \\[1em] &= \frac{120}{0.50} \\[1em] &= 240 \, \text{Hz} \end{aligned} \]

Thus, the frequency of the waves is 240 Hz.

Explanation:

The correct answer is: A

The electric field between parallel plates is mostly uniform, but not everywhere. Near the edges, the field spreads out, which is called edge effect. Because of this, the field cannot be perfectly uniform everywhere between the plates.

Here's why the other answers are incorrect:

• B. True — the field strength depends on the amount of charge on the plates.


• C. True — more charge means a stronger electric field.


• D. True — outside the plates, the electric field is nearly zero except at the edges.

The correct answer is: C

Topic: Relative Velocity

The velocity of \( P \) relative to \( Q \), denoted \( v_{PQ} \), is given by:

\[ v_{PQ} = v_P - v_Q \]

Substituting the given velocities:

\[ v_{PQ} = 30\ \mathrm{m\,s^{-1}} - 20\ \mathrm{m\,s^{-1}} \]

Calculating the difference:

\[ v_{PQ} = 10\ \mathrm{m\,s^{-1}} \]

This means car \( P \) is moving at \( 10\ \mathrm{m\,s^{-1}} \) faster than car \( Q \) in the same direction.

The correct answer is: C

Topic: Electromagnetic Spectrum – Infrared Waves

The wavelength of infrared radiation lies within the range:

\[ 10^{-3}\ \mathrm{m} \quad \text{to} \quad 10^{-6}\ \mathrm{m} \]

This means the wavelength is longer than \(10^{-6}\ \mathrm{m}\) and shorter than \(10^{-3}\ \mathrm{m}\).

Therefore, the correct statement is that the wavelength is longer than \(10^{-6}\ \mathrm{m}\).

Explanation:

The correct answer is: D

When an electron moves from a higher energy level to a lower one, it loses energy. This lost energy is released as a photon.

Here's why the other answers are incorrect:

• A. Incorrect — absorption happens when the electron moves to a higher level.


• B. Incorrect — only one photon is emitted in a single jump.


• C. Incorrect — electrons do not absorb photons when moving down to a lower level.

Explanation:

The correct answer is: D

Both bodies experience the same force for the same time. This gives them the same impulse (Force × time), which means both gain the same momentum.

Here's why the other answers are incorrect:

• A & B. Incorrect — neither body gets more momentum, they gain the same amount.


• C. Incorrect — the lighter body gets a higher velocity, but momentum is the same.

Explanation:

The correct answer is: B

A step-up transformer needs a changing magnetic field to work. Only alternating current (AC) can create this changing magnetic field.

Here's why the other answers are incorrect:

• A. Lead-acid accumulator stores DC, not AC.


• C. Moving-coil galvanometer measures small DC currents.


• D. Induction coil can work with DC when switched but is not AC-only.

Explanation:

The correct answer is: B

Topic: Equations of Motion

The equation for distance travelled under uniform acceleration is:

\[ S = ut + \frac{1}{2} a t^2 \]

Given initial velocity \( u = 20 \, \text{m/s} \) and time \( t = 15 \, \text{s} \), substitute:

\[ S = 20 \times 15 + \frac{1}{2} a \times 15^2 \]

Calculate the terms:

\[ S = 300 + \frac{1}{2} a \times 225 \]

Simplify the expression:

\[ S = 300 + \frac{225a}{2} \]

This matches option B.

Explanation:

The correct answer is: B

Topic: Projectile Motion

For a projectile, the maximum range \( R \) and maximum height \( H \) are given by:

\[ R = \frac{u^2 \sin(2\theta)}{g}, \quad H = \frac{u^2 \sin^2\theta}{2g} \]

Taking the ratio:

\[ \frac{R}{H} = \frac{ \frac{u^2 \sin(2\theta)}{g} }{ \frac{u^2 \sin^2\theta}{2g} } = \frac{2 \sin(2\theta)}{\sin^2\theta} \]

Given \( \frac{R}{H} = 4 \), substitute and simplify:

\[ \frac{2 \sin(2\theta)}{\sin^2\theta} = 4 \Rightarrow \frac{ \sin(2\theta) }{ \sin^2\theta } = 2 \]

Using the identity \( \sin(2\theta) = 2\sin\theta\cos\theta \):

\[ \frac{2 \sin\theta \cos\theta}{\sin^2\theta} = 2 \]

\[ \Rightarrow \frac{2 \cos\theta}{\sin\theta} = 2 \]

\[ \Rightarrow \cot\theta = 1 \]

Therefore, \( \theta = 45^\circ \).

Explanation:

The correct answer is: A

According to Newton's Third Law of Motion, every action force has an equal and opposite reaction force.

So the force the towing vehicle exerts on the bus is equal in magnitude and opposite in direction to the force the bus exerts back on the towing vehicle. This matches statement II.

Here's why the other statements are incorrect:

• I. Incorrect — The force the bus exerts on the road is not related to the force between the bus and the towing vehicle.


• III. Incorrect — The forces between the bus and the towing vehicle are equal, not greater or smaller.


• IV. Incorrect — The force the road exerts on the towing vehicle is a different interaction (road–vehicle), not vehicle–bus.

Explanation:

The correct answer is: C

The distance between X and Y is the area under the velocity-time graph from \( t = 4 \, \text{s} \) to \( t = 8 \, \text{s} \). The velocity is constant at 40 m/s, so the area is a rectangle:

\[ \begin{aligned} \text{Area} &= \text{velocity} \times \text{time} \\[1em] &= 40 \, \text{m/s} \times (8 - 4) \, \text{s} \\[1em] &= 40 \times 4 \\[1em] &= 160 \, \text{m} \end{aligned} \]

Thus, the distance is 160.0 m.