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Question 1Physics

A body moves along a straight line with uniform acceleration. Its velocity increases from 5 m/s to 25 m/s in 4 s. What is the acceleration?

  1. 6 m/s²
  2. 7.5 m/s²
  3. 5 m/s² Correct answer.
  4. 4 m/s²

Explanation

Acceleration is the rate of change of velocity, a = (v − u)/t. Substituting gives (25 − 5)/4 = 20/4 = 5 m/s². The value is positive because the velocity is increasing along the chosen positive direction.

Question 2Physics

A projectile is launched with speed u at angle θ to the horizontal on level ground, with air resistance neglected. Which expression gives its horizontal range?

  1. 2u² sin θ / g
  2. u² sin²θ / (2g)
  3. u² sin 2θ / g Correct answer.
  4. u² cos 2θ / g

Explanation

Time of flight is 2u sinθ/g and horizontal velocity is u cosθ, so range R = (u cosθ)(2u sinθ/g) = u² sin2θ/g. This peaks at θ = 45° and vanishes at 0° and 90°, as expected physically.

Question 3Physics

A block of mass 4 kg rests on a rough horizontal floor with coefficient of static friction 0.5. Taking g = 10 m/s², what is the minimum horizontal force needed to just start sliding?

  1. 2 N
  2. 40 N
  3. 20 N Correct answer.
  4. 8 N

Explanation

The limiting static friction equals μ times the normal reaction, f = μmg. Here f = 0.5 × 4 × 10 = 20 N, so a slightly larger applied force starts motion. Until that value is reached, static friction simply matches the applied force.

Question 4Physics

A particle moves in a circle of radius 2 m at a constant speed of 6 m/s. What is the magnitude of its centripetal acceleration?

  1. 18 m/s² Correct answer.
  2. 36 m/s²
  3. 3 m/s²
  4. 12 m/s²

Explanation

Centripetal acceleration has magnitude v²/r for uniform circular motion. Substituting gives 36/2 = 18 m/s², directed toward the centre of the circle. The speed is constant, but the velocity direction changes continuously.

Question 5Physics

A force of 10 N acts on a body and displaces it by 3 m. The work done is zero. What is the angle between the force and the displacement?

  1. 90° Correct answer.
  2. 0°
  3. 60°
  4. 180°

Explanation

Work is W = Fs cosθ, so zero work with non-zero force and displacement requires cosθ = 0. That happens at θ = 90°, where the force is perpendicular to the displacement. A body in circular motion at constant speed is the classic example.

Question 6Physics

Two bodies of masses m and 2m have equal kinetic energies. What is the ratio of their linear momenta, p(m) : p(2m)?

  1. √2 : 1 Correct answer.
  2. 2 : 1
  3. 1 : √2
  4. 1 : 2

Explanation

Since K = p²/(2m), equal kinetic energies give p² proportional to m, so p ∝ √m. Hence the lighter body has momentum in the ratio √m : √(2m), that is √2 : 1. The lighter body must move faster to carry the same energy.

Question 7Physics

A uniform metre rule is pivoted at its centre and balances. A 20 g mass is hung 30 cm from the pivot on one side. Where must a 30 g mass be hung on the other side to keep balance?

  1. 30 cm from the pivot
  2. 15 cm from the pivot
  3. 45 cm from the pivot
  4. 20 cm from the pivot Correct answer.

Explanation

For rotational equilibrium about the pivot, clockwise and anticlockwise moments must be equal: 20 × 30 = 30 × d. Solving gives d = 600/30 = 20 cm. The heavier mass therefore sits closer to the pivot.

Question 8Physics

A satellite orbits Earth in a circular orbit of radius r. If the radius is increased to 4r, the orbital speed becomes:

  1. unchanged
  2. twice the original value
  3. one quarter of the original value
  4. half the original value Correct answer.

Explanation

For a circular orbit, gravity supplies the centripetal force: GMm/r² = mv²/r, so v = √(GM/r). Speed therefore varies as 1/√r, and increasing r fourfold halves the speed. The period, by contrast, increases eightfold.

Question 9Physics

The escape velocity from Earth's surface is about 11.2 km/s. What is the escape velocity from a planet having the same density but twice Earth's radius?

  1. 5.6 km/s
  2. 11.2 km/s
  3. 15.8 km/s
  4. 22.4 km/s Correct answer.

Explanation

Escape velocity is v = √(2GM/R). With uniform density, M ∝ R³, so v ∝ R. Doubling the radius while keeping density fixed therefore doubles the escape velocity to 22.4 km/s.

Question 10Physics

A wire of length L and cross-sectional area A has Young's modulus Y. It is stretched by a force F. The extension produced is:

  1. FL/(AY) Correct answer.
  2. AY/(FL)
  3. F/(LAY)
  4. FAY/L

Explanation

Young's modulus is defined as stress divided by strain, Y = (F/A)/(ΔL/L). Rearranging gives the extension ΔL = FL/(AY). A stiffer or thicker wire therefore stretches less under the same load.

Question 11Physics

A body floats with 60% of its volume submerged in a liquid. What is the ratio of the density of the body to that of the liquid?

  1. 0.6 Correct answer.
  2. 1.0
  3. 0.4
  4. 1.67

Explanation

For a floating body, the weight equals the weight of displaced liquid, so ρ_body V g = ρ_liquid V_submerged g. Hence ρ_body/ρ_liquid = V_submerged/V = 0.6. The body is less dense than the liquid, as floating requires.

Question 12Physics

Water flows steadily through a horizontal pipe whose cross-section narrows from area A to A/3. If the speed in the wider section is v, the speed in the narrow section is:

  1. 3v Correct answer.
  2. v/3
  3. 9v
  4. v

Explanation

The equation of continuity for an incompressible fluid gives A₁v₁ = A₂v₂. With the area reduced to one third, the speed must rise to 3v to keep the volume flow rate constant. By Bernoulli's principle the pressure then falls in the narrow section.

Question 13Physics

A simple pendulum has a period of 2 s on Earth. On a planet where acceleration due to gravity is four times that on Earth, its period becomes:

  1. 1 s Correct answer.
  2. 8 s
  3. 4 s
  4. 0.5 s

Explanation

The period of a simple pendulum is T = 2π√(L/g), so T varies as 1/√g. Quadrupling g halves the period, giving 1 s. The period is independent of the mass of the bob.

Question 14Physics

A particle executes simple harmonic motion with amplitude A. At what displacement from the mean position is its kinetic energy equal to its potential energy?

  1. A/2
  2. A/√2 Correct answer.
  3. A√2
  4. A/4

Explanation

Total energy is ½kA², and potential energy is ½kx². Setting ½kx² = ½ × ½kA² gives x² = A²/2, so x = A/√2. At this point velocity is neither maximum nor zero.

Question 15Physics

The speed of sound in a gas at constant pressure varies with absolute temperature T as:

  1. T
  2. T²
  3. √T Correct answer.
  4. 1/√T

Explanation

For an ideal gas, v = √(γRT/M), so the speed of sound depends on the square root of absolute temperature. Raising the temperature from 300 K to 1200 K therefore doubles the speed. The relation holds at constant pressure because density falls as temperature rises.

Question 16Physics

A stationary observer hears a source of frequency 500 Hz approaching with a speed equal to one tenth the speed of sound. What frequency is heard?

  1. 556 Hz Correct answer.
  2. 455 Hz
  3. 500 Hz
  4. 550 Hz

Explanation

For an approaching source the observed frequency is f' = f v/(v − v_s). With v_s = 0.1v, f' = 500/(0.9) ≈ 556 Hz. The pitch rises as the source approaches and falls after it passes.

Question 17Physics

Two identical resistors, each of 6 Ω, are connected in parallel across a 12 V battery of negligible internal resistance. What total current flows from the battery?

  1. 3 A
  2. 4 A Correct answer.
  3. 1 A
  4. 2 A

Explanation

Two equal resistors in parallel give an equivalent resistance of 3 Ω. The total current is then I = V/R = 12/3 = 4 A, which splits equally as 2 A through each branch.

Question 18Physics

A wire of resistance R is stretched uniformly to twice its original length. Assuming volume is conserved, its new resistance is:

  1. 4R Correct answer.
  2. 8R
  3. 2R
  4. R/2

Explanation

Stretching to double length halves the cross-sectional area because volume is constant. Since R = ρL/A, doubling L and halving A multiplies resistance by four. The result is 4R.

Question 19Physics

Three capacitors of 3 μF each are connected in series. What is the equivalent capacitance?

  1. 9 μF
  2. 1 μF Correct answer.
  3. 3 μF
  4. 1.5 μF

Explanation

For capacitors in series, 1/C = 1/C₁ + 1/C₂ + 1/C₃, so 1/C = 1/3 + 1/3 + 1/3 = 1. Hence C = 1 μF. Series connection always gives a value smaller than the smallest individual capacitor.

Question 20Physics

A charged particle enters a uniform magnetic field with velocity parallel to the field. Its path in the field is:

  1. a parabola
  2. a helix along the field direction
  3. a circle of constant radius
  4. a straight line with unchanged speed Correct answer.

Explanation

The magnetic force is F = qvB sinθ, which vanishes when the velocity is parallel to the field (θ = 0). With no force there is no acceleration, so the particle continues in a straight line at constant speed. Circular or helical paths require a component of velocity perpendicular to the field.

Question 21Physics

A step-down transformer has 1000 turns in the primary and 200 turns in the secondary. If the primary is supplied with 220 V AC, the secondary voltage is:

  1. 44 V Correct answer.
  2. 55 V
  3. 220 V
  4. 1100 V

Explanation

For an ideal transformer, V_s/V_p = N_s/N_p. Thus V_s = 220 × 200/1000 = 44 V, a step-down as expected from the smaller secondary turns. The current in the secondary rises in the same proportion that the voltage falls.

Question 22Physics

In a Young's double-slit experiment, the fringe width is β. If the separation between the slits is doubled while everything else is unchanged, the new fringe width is:

  1. 4β
  2. 2β
  3. β/2 Correct answer.
  4. β

Explanation

Fringe width is β = λD/d, so it is inversely proportional to the slit separation d. Doubling d therefore halves the fringe width to β/2. Increasing the wavelength or screen distance would widen the fringes instead.

Question 23Physics

A convex lens of focal length 20 cm forms a real image of an object placed 30 cm from it. The image distance is:

  1. 60 cm Correct answer.
  2. 30 cm
  3. 20 cm
  4. 12 cm

Explanation

Using the lens formula 1/f = 1/v − 1/u with u = −30 cm and f = +20 cm gives 1/v = 1/20 − 1/30 = 1/60. Hence v = 60 cm, a real image formed beyond 2f, which is magnified and inverted.

Question 24Physics

Light of wavelength 500 nm falls on a metal surface whose work function is 2.0 eV. Taking hc = 1240 eV·nm, the maximum kinetic energy of the emitted photoelectrons is:

  1. 2.48 eV
  2. 0.48 eV Correct answer.
  3. 0.96 eV
  4. 1.24 eV

Explanation

Photon energy is E = hc/λ = 1240/500 = 2.48 eV. Einstein's photoelectric equation gives K_max = E − φ = 2.48 − 2.0 = 0.48 eV. Since this is positive, emission occurs.

Question 25Physics

In a hydrogen atom, an electron falls from the n = 3 level to the n = 2 level. The emitted photon belongs to which spectral series?

  1. Brackett series
  2. Balmer series Correct answer.
  3. Paschen series
  4. Lyman series

Explanation

Spectral series are named by the lower level of the transition. Transitions ending at n = 2 form the Balmer series, which lies mostly in the visible region. The n = 3 to n = 2 line is the H-alpha line at about 656 nm.

Question 26Physics

A car travels the first half of a straight road at 40 km/h and the second half at 60 km/h. What is its average speed for the whole journey?

  1. 50 km/h
  2. 48 km/h Correct answer.
  3. 45 km/h
  4. 52 km/h

Explanation

For equal distances the average speed is the harmonic mean 2v1v2/(v1+v2), not the arithmetic mean, because more time is spent at the slower speed. Substituting gives 2(40)(60)/100 = 48 km/h.

Question 27Physics

A projectile is launched at an angle of 45° to the horizontal with speed u over level ground. Ignoring air resistance, what is its horizontal range?

  1. u²/(2g)
  2. u²/g Correct answer.
  3. 2u²/g
  4. u²/(4g)

Explanation

Range R = u² sin2θ / g, and sin90° = 1 at θ = 45°, giving R = u²/g. This is the maximum possible range for a given launch speed over level ground.

Question 28Physics

A block of mass 5 kg rests on a rough horizontal floor with coefficient of static friction 0.4. Taking g = 10 m/s², what is the minimum horizontal force needed to just start the block moving?

  1. 50 N
  2. 20 N Correct answer.
  3. 10 N
  4. 2 N

Explanation

The limiting static friction is f = μN = μmg since the normal reaction equals the weight on a horizontal floor. Thus f = 0.4 × 5 × 10 = 20 N, and this is the minimum applied force to initiate motion.

Question 29Physics

A body of mass 2 kg moving at 3 m/s collides head-on with a stationary body of mass 4 kg and sticks to it. What is the speed of the combined body immediately after the collision?

  1. 1.5 m/s
  2. 2 m/s
  3. 3 m/s
  4. 1 m/s Correct answer.

Explanation

In a perfectly inelastic collision only momentum is conserved: (2)(3) = (2+4)v, so v = 6/6 = 1 m/s. Kinetic energy is not conserved here, which is why the answer is below the initial speed.

Question 30Physics

A flywheel of moment of inertia 4 kg·m² is acted on by a constant torque of 12 N·m from rest. What is its angular speed after 3 s?

  1. 36 rad/s
  2. 9 rad/s Correct answer.
  3. 4 rad/s
  4. 3 rad/s

Explanation

Angular acceleration α = τ/I = 12/4 = 3 rad/s². Starting from rest, ω = αt = 3 × 3 = 9 rad/s.

Question 31Physics

The acceleration due to gravity at a height h above Earth's surface, where h is small compared with Earth's radius R, decreases approximately by what fraction of its surface value?

  1. h/R
  2. h²/R²
  3. h/(2R)
  4. 2h/R Correct answer.

Explanation

Using g' = g(1 + h/R)^-2 and the binomial expansion for small h/R gives g' ≈ g(1 - 2h/R). The fractional decrease is therefore about 2h/R.

Question 32Physics

An ideal gas undergoes an isothermal expansion at temperature T. Which statement about the gas is correct?

  1. Its internal energy decreases by the heat it absorbs.
  2. Its internal energy increases by the work done on it.
  3. Its internal energy stays constant and it absorbs heat equal to the work done. Correct answer.
  4. It absorbs no heat and its temperature falls.

Explanation

For an ideal gas the internal energy depends only on temperature, so an isothermal process keeps ΔU = 0. The first law then gives Q = W, meaning the heat absorbed equals the work done by the gas.

Question 33Physics

A body of specific heat capacity 500 J/(kg·K) and mass 2 kg is heated so that its temperature rises by 10 K. How much heat is absorbed?

  1. 2500 J
  2. 5000 J
  3. 10000 J Correct answer.
  4. 1000 J

Explanation

Heat absorbed Q = mcΔT = 2 × 500 × 10 = 10000 J. Specific heat capacity is the energy needed per kilogram per kelvin.

Question 34Physics

Sound waves travel from air into water. Which quantity remains unchanged across the boundary?

  1. Amplitude
  2. Frequency Correct answer.
  3. Wavelength
  4. Speed

Explanation

Frequency is set by the source and stays the same when a wave crosses into a new medium. Speed and wavelength both change because the wave speed is different in water, and amplitude changes with transmission.

Question 35Physics

Two point charges of +4 μC and -4 μC are separated by 0.2 m in vacuum. Taking 1/(4πε₀) = 9 × 10⁹ N·m²/C², what is the magnitude of the force between them?

  1. 3.6 N Correct answer.
  2. 0.36 N
  3. 7.2 N
  4. 36 N

Explanation

Coulomb's law gives F = kq₁q₂/r² = (9 × 10⁹)(4 × 10⁻⁶)(4 × 10⁻⁶)/(0.2)². This equals 1.44 × 10⁻¹/0.04 = 3.6 N, and the force is attractive because the charges are opposite.

Question 36Physics

A 12 V cell has internal resistance 1 Ω and supplies a 5 Ω resistor. A second 5 Ω resistor is then connected in parallel with the first. What happens to the cell's terminal voltage?

  1. It rises from 10 V to 12 V.
  2. It remains 10 V.
  3. It falls from 10 V to 60/7 V. Correct answer.
  4. It falls from 10 V to 6 V.

Explanation

Initially current is 12/(5+1) = 2 A, so terminal voltage is 10 V. The parallel load is 2.5 Ω; current becomes 24/7 A and terminal voltage is 12 - 24/7 = 60/7 V.

Question 37Physics

A galvanometer of resistance 50 Ω gives full-scale deflection at 1 mA. What shunt resistance converts it into an ammeter reading up to 1 A?

  1. About 0.5 Ω
  2. About 500 Ω
  3. About 50 Ω
  4. About 0.05 Ω Correct answer.

Explanation

The shunt carries the excess current I - Ig = 0.999 A while the galvanometer carries 0.001 A at full scale. Since both are in parallel, S = IgG/(I - Ig) ≈ (0.001 × 50)/0.999 ≈ 0.05 Ω.

Question 38Physics

A charged particle of charge q and mass m moves with speed v in a circle of radius r in a uniform magnetic field B. What is the time period of its circular motion?

  1. qB/(2πm)
  2. 2πmB/q
  3. 2πr/v dependent on speed
  4. 2πm/(qB) Correct answer.

Explanation

Setting qvB = mv²/r gives r = mv/(qB), and the period is T = 2πr/v = 2πm/(qB). The period is independent of speed and radius for non-relativistic motion.

Question 39Physics

An alternating voltage is given by V = 200 sin(100πt) volts. What is its rms value?

  1. About 282 V
  2. 200 V
  3. About 100 V
  4. About 141 V Correct answer.

Explanation

The peak value is 200 V, so the rms value is V₀/√2 = 200/1.414 ≈ 141 V. The angular frequency 100π rad/s sets the frequency at 50 Hz but does not affect the rms value.

Question 40Physics

A ray of light passes from glass of refractive index 1.5 into air. What is the critical angle for total internal reflection?

  1. About 42° Correct answer.
  2. About 60°
  3. About 48°
  4. About 30°

Explanation

The critical angle satisfies sin C = 1/n = 1/1.5 = 0.667, giving C ≈ 42°. Beyond this angle of incidence, light is totally internally reflected into the glass.

Question 41Physics

In a compound microscope the objective has a very short focal length and the eyepiece acts as a simple magnifier. Where should the final image formed by the eyepiece be located for comfortable viewing?

  1. At infinity, with the object for the eyepiece at its focus Correct answer.
  2. At the eyepiece itself, giving zero magnification
  3. At the objective's focus, giving maximum magnification
  4. At the near point of the eye, with the object inside the focal length

Explanation

Relaxed viewing uses the eyepiece with the intermediate image at its focal plane so the final image is at infinity. This gives comfortable, strain-free observation, while placing the image at the near point gives slightly more magnification but more eye strain.

Question 42Physics

The de Broglie wavelength of an electron accelerated through a potential difference V is proportional to which quantity?

  1. 1/V
  2. √V
  3. V
  4. 1/√V Correct answer.

Explanation

The kinetic energy is eV = p²/2m, so p = √(2meV) and λ = h/p ∝ 1/√V. Doubling the accelerating voltage therefore reduces the wavelength by a factor of √2.

Question 43Physics

A radioactive sample has a half-life of 10 days. What fraction of the original nuclei remains undecayed after 30 days?

  1. 1/16
  2. 1/3
  3. 1/8 Correct answer.
  4. 1/6

Explanation

Thirty days is three half-lives, so the surviving fraction is (1/2)³ = 1/8. Each half-life halves the number of undecayed nuclei.

Question 44Physics

In a p-n junction diode, what happens to the width of the depletion region when it is forward biased?

  1. It decreases, lowering the barrier potential Correct answer.
  2. It increases, raising the barrier potential
  3. It stays the same because doping is unchanged
  4. It disappears completely at zero bias

Explanation

Forward bias applies a potential opposing the built-in barrier, so majority carriers are pushed toward the junction and the depletion width shrinks. The reduced barrier allows a large forward current once it exceeds about 0.7 V in silicon.

Question 45Physics

A body is projected vertically upwards with speed u. Taking air resistance as negligible, at what height is its speed equal to u/2?

  1. u²/(2g)
  2. 3u²/(2g)
  3. 3u²/(8g) Correct answer.
  4. u²/(8g)

Explanation

Using v² = u² - 2gh with v = u/2 gives u²/4 = u² - 2gh, so 2gh = 3u²/4 and h = 3u²/(8g). This is three-quarters of the maximum height u²/(2g).

Question 46Physics

A particle executes SHM with angular frequency ω and amplitude A. What is its speed at the position where its displacement is A/2 from the mean position?

  1. (√3/2)ωA Correct answer.
  2. (1/2)ωA√2
  3. ωA/2
  4. ωA

Explanation

For SHM, v = ω√(A² - x²). With x = A/2, v = ω√(A² - A²/4) = ωA√3/2. The speed is maximum at the mean position and zero at the extremes.

Question 47Physics

A vessel contains a mixture of 2 moles of helium and 3 moles of oxygen at temperature T. Treating both as ideal, what is the ratio of the average translational kinetic energy per helium molecule to that per oxygen molecule?

  1. 4 : 1
  2. 1 : 1 Correct answer.
  3. 2 : 1
  4. 1 : 2

Explanation

The average translational kinetic energy per molecule is (3/2)kT for any ideal gas, depending only on temperature. Since both gases are at the same temperature, the ratio is 1 : 1 regardless of molecular mass.

Question 48Physics

A parallel plate capacitor is charged and then disconnected from the battery. A dielectric slab of constant K is then inserted to fill the gap. How do the electric field and stored energy change?

  1. Field falls to E/K and energy falls to U/K Correct answer.
  2. Field rises to KE and energy rises to KU
  3. Field stays E and energy rises to KU
  4. Field falls to E/K and energy stays U

Explanation

With the battery disconnected the free charge is fixed, so D is unchanged and E = D/(ε₀K) falls to E/K. The energy U = Q²/(2C) falls to U/K because the capacitance rises to KC.

Question 49Physics

A charged particle moves undeflected through a region where a uniform electric field E and a uniform magnetic field B are mutually perpendicular and both perpendicular to its velocity. What is its speed?

  1. B/E
  2. EB
  3. E/B Correct answer.
  4. E/(B²)

Explanation

For zero net deflection the electric force qE must balance the magnetic force qvB, so v = E/B. This velocity-selection condition underlies devices such as the Thomson cathode-ray experiment.

Question 50Physics

In a series LCR circuit at resonance, the voltage across the inductor leads the current by 90° and the voltage across the capacitor lags by 90°. What is the phase relationship between the applied voltage and the current?

  1. The current leads the applied voltage by 45°
  2. They are in phase, and the impedance equals R Correct answer.
  3. The current leads the applied voltage by 90°
  4. The current lags the applied voltage by 90°

Explanation

At resonance the reactances cancel, XL = XC, so the net reactance is zero and the impedance is purely resistive, equal to R. The applied voltage and current are therefore in phase and the power factor is unity.