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Question 1Physics

A body moves along a straight line with uniform acceleration. Which quantity is represented by the slope of its velocity–time graph?

  1. Jerk
  2. Displacement
  3. Acceleration Correct answer.
  4. Average speed

Explanation

On a velocity–time graph the vertical axis is velocity and the horizontal axis is time, so the slope equals the rate of change of velocity, which is acceleration. The area under the same graph gives displacement, not the slope.

Question 2Physics

A stone is dropped from rest from a tower and falls freely under gravity. Taking g = 10 m/s², how far does it fall in the first 3 s?

  1. 45 m Correct answer.
  2. 90 m
  3. 15 m
  4. 30 m

Explanation

For free fall from rest, distance s = ½gt². Substituting gives s = ½ × 10 × 3² = 45 m. The value 30 m would come from using gt instead of ½gt².

Question 3Physics

A projectile is launched at speed u at angle θ to the horizontal on level ground, with air resistance neglected. Which statement about its motion is correct?

  1. Both components of velocity remain constant during the flight
  2. The vertical component of velocity stays constant throughout the flight
  3. The horizontal component of velocity changes uniformly with time
  4. The horizontal component of velocity remains constant while the vertical component changes uniformly Correct answer.

Explanation

With air resistance neglected, the only force is weight, which acts vertically. Hence horizontal velocity is unchanged and the vertical velocity changes at the constant rate g.

Question 4Physics

Two forces of magnitudes 6 N and 8 N act at a single point at right angles to each other. What is the magnitude of their resultant?

  1. 10 N Correct answer.
  2. 48 N
  3. 2 N
  4. 14 N

Explanation

Perpendicular vectors add by the parallelogram rule, giving R = √(6² + 8²) = √100 = 10 N. Simple addition applies only when the forces are parallel and in the same direction.

Question 5Physics

A body of mass 4 kg experiences a net force of 12 N. What is the magnitude of its acceleration?

  1. 48 m/s²
  2. 0.33 m/s²
  3. 3 m/s² Correct answer.
  4. 16 m/s²

Explanation

Newton's second law gives a = F/m. Dividing 12 N by 4 kg yields 3 m/s², and the acceleration is in the direction of the net force.

Question 6Physics

A block slides down a rough inclined plane at constant velocity. Which statement correctly describes the forces on the block along the plane?

  1. The normal reaction equals the component of weight along the plane
  2. Kinetic friction acts down the plane, aiding the motion
  3. The component of weight along the plane exceeds the kinetic friction
  4. The component of weight along the plane equals the kinetic friction Correct answer.

Explanation

Constant velocity means zero acceleration, so the net force along the plane is zero. The downslope component of weight must therefore be exactly balanced by kinetic friction acting up the slope.

Question 7Physics

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. 3 m/s²
  2. 18 m/s² Correct answer.
  3. 12 m/s²
  4. 72 m/s²

Explanation

Centripetal acceleration is a = v²/r. Substituting v = 6 m/s and r = 2 m gives 36/2 = 18 m/s², directed toward the centre of the circle.

Question 8Physics

A spring of force constant 200 N/m is stretched by 5 cm from its natural length. What elastic potential energy is stored?

  1. 0.25 J Correct answer.
  2. 0.50 J
  3. 5 J
  4. 10 J

Explanation

Elastic potential energy is U = ½kx². With k = 200 N/m and x = 0.05 m, U = ½ × 200 × 0.0025 = 0.25 J. The extension must be converted to metres before substitution.

Question 9Physics

Two bodies of masses m and 3m move toward each other with equal speeds and stick together after colliding. What is the velocity of the combined body?

  1. Zero
  2. v/2 in the direction of the lighter body
  3. v in the direction of the heavier body
  4. v/2 in the direction of the heavier body Correct answer.

Explanation

Taking the heavier body's direction as positive, total momentum is 3mv − mv = 2mv. The combined mass is 4m, so the final velocity is 2mv/4m = v/2 in the direction of the heavier body.

Question 10Physics

A flywheel of moment of inertia 2 kg·m² is acted on by a constant torque of 8 N·m. What is its angular acceleration?

  1. 16 rad/s²
  2. 4 rad/s² Correct answer.
  3. 6 rad/s²
  4. 0.25 rad/s²

Explanation

For rotational motion, torque equals moment of inertia times angular acceleration, so α = τ/I. Dividing 8 N·m by 2 kg·m² gives 4 rad/s².

Question 11Physics

A solid sphere and a hollow cylinder of the same mass and radius roll without slipping down the same incline from rest. Which reaches the bottom first?

  1. It depends on the length of the incline
  2. Both arrive together
  3. The solid sphere Correct answer.
  4. The hollow cylinder

Explanation

The acceleration down an incline is g sinθ/(1 + I/mR²). The solid sphere has the smaller moment of inertia factor (2/5), so it has the larger acceleration and arrives first, independent of incline length.

Question 12Physics

The acceleration due to gravity at the surface of a planet is g. At a height equal to the planet's radius above its surface, what is the acceleration due to gravity?

  1. g/4 Correct answer.
  2. g/16
  3. g/2
  4. g/9

Explanation

Gravity follows an inverse-square law in distance from the centre. At a height equal to the radius, the distance from the centre doubles, so the acceleration becomes g/2² = g/4.

Question 13Physics

A satellite is in a circular orbit around the Earth. If its orbital radius is increased, what happens to its orbital speed?

  1. It stays the same
  2. It decreases Correct answer.
  3. It becomes zero
  4. It increases

Explanation

Equating gravitational force to the centripetal requirement gives v = √(GM/r). Since r appears in the denominator, a larger orbital radius means a smaller orbital speed.

Question 14Physics

A steel wire of length L and cross-sectional area A stretches by an amount e under a load. If a wire of the same material but twice the length and half the area is loaded identically, the extension becomes:

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

Explanation

Extension is e = FL/(AY). Doubling L doubles the extension, and halving A doubles it again, so the combined factor is four. Hence the new extension is 4e.

Question 15Physics

Water flows through a horizontal pipe whose cross-sectional area narrows to one third of its original value. How does the flow speed in the narrow section compare with the wider section?

  1. Unchanged
  2. Nine times as large
  3. One third as large
  4. Three times as large Correct answer.

Explanation

For an incompressible fluid the equation of continuity gives A₁v₁ = A₂v₂. Reducing the area by a factor of three must raise the speed by the same factor, so the narrow section has triple the speed.

Question 16Physics

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

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

Explanation

For a floating body, the weight of displaced liquid equals the body's weight, so the density ratio equals the fraction of volume submerged. That fraction is 0.6, giving a ratio of 0.6.

Question 17Physics

The temperature of an ideal gas is doubled at constant volume. What happens to the root-mean-square speed of its molecules?

  1. It increases by a factor of √2 Correct answer.
  2. It stays the same
  3. It doubles
  4. It quadruples

Explanation

The root-mean-square speed depends on absolute temperature as v ∝ √T. Doubling the absolute temperature therefore multiplies the rms speed by √2, not by 2.

Question 18Physics

An ideal gas undergoes an isothermal expansion. Which statement about the heat absorbed and work done is correct?

  1. Heat absorbed equals the work done by the gas Correct answer.
  2. Work done is zero
  3. Heat absorbed is less than the work done
  4. Heat absorbed is zero

Explanation

For an ideal gas the internal energy depends only on temperature, so an isothermal process has zero change in internal energy. The first law then gives Q = W, so heat absorbed equals work done by the gas.

Question 19Physics

A simple pendulum has a period of 2 s on Earth. What is its period on a planet where the acceleration due to gravity is one quarter of that on Earth?

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

Explanation

The period of a simple pendulum is T = 2π√(L/g), so T is inversely proportional to √g. Reducing g by a factor of four multiplies the period by two, giving 4 s.

Question 20Physics

Two identical progressive waves travelling in opposite directions superpose in a medium. What is produced?

  1. A wave of half the original frequency
  2. A travelling wave of double amplitude
  3. A stationary wave with nodes and antinodes Correct answer.
  4. No disturbance at all

Explanation

Superposition of two identical waves moving in opposite directions gives a stationary wave. Points of zero displacement are nodes and points of maximum displacement are antinodes, spaced a quarter wavelength apart.

Question 21Physics

A source of sound moves toward a stationary observer. Compared with the emitted sound, the observed sound has:

  1. A higher frequency and shorter wavelength Correct answer.
  2. The same frequency but a shorter wavelength
  3. A higher frequency and longer wavelength
  4. A lower frequency and longer wavelength

Explanation

Approach compresses successive wavefronts, shortening the wavelength in front of the source. Because the wave speed in air is unchanged, the shorter wavelength corresponds to a higher observed frequency.

Question 22Physics

Two point charges are separated by a distance r in vacuum. If the separation is doubled while the charges are unchanged, the electrostatic force becomes:

  1. One quarter of the original Correct answer.
  2. Twice the original
  3. Four times the original
  4. Half the original

Explanation

Coulomb's law gives force proportional to 1/r². Doubling the separation therefore divides the force by four, leaving one quarter of its original magnitude.

Question 23Physics

Three resistors of 2 Ω, 3 Ω and 6 Ω are connected in parallel. What is the equivalent resistance of the combination?

  1. 0.5 Ω
  2. 3 Ω
  3. 1 Ω Correct answer.
  4. 11 Ω

Explanation

For parallel resistors, 1/R = 1/2 + 1/3 + 1/6 = 3/6 + 2/6 + 1/6 = 1, so R = 1 Ω. The equivalent resistance is always smaller than the smallest individual resistor.

Question 24Physics

A charged particle enters a uniform magnetic field with its velocity parallel to the field lines. What path does it follow?

  1. A straight line with unchanged speed Correct answer.
  2. A circle in the plane perpendicular to the field
  3. A helix around the field lines
  4. A parabola bending along the field

Explanation

The magnetic force is qv × B, which vanishes when velocity and field are parallel. With no force acting, the particle continues in a straight line at constant speed.

Question 25Physics

In a step-down transformer that is ideal, the secondary voltage is 20 V when the primary is supplied with 200 V. If the primary current is 0.5 A, what is the secondary current?

  1. 0.5 A
  2. 50 A
  3. 0.05 A
  4. 5 A Correct answer.

Explanation

An ideal transformer conserves power, so VₚIₚ = VₛIₛ. The primary power is 200 × 0.5 = 100 W, and dividing by 20 V gives a secondary current of 5 A.

Question 26Physics

A body starts from rest and moves with uniform acceleration of 4 m/s². How far does it travel in the first 3 seconds?

  1. 36 m
  2. 24 m
  3. 18 m Correct answer.
  4. 12 m

Explanation

Using s = ut + ½at² with u = 0, a = 4 m/s² and t = 3 s, we get s = ½ × 4 × 9 = 18 m. The squared time factor means distance grows rapidly with time.

Question 27Physics

A projectile is launched at 45° to the horizontal with speed u over level ground, neglecting air resistance. Which launch angle gives the same horizontal range?

  1. 30° Correct answer.
  2. 15°
  3. 60°
  4. 90°

Explanation

Range for a projectile on level ground is R = u² sin2θ / g, which depends only on sin2θ. Angles θ and 90° − θ give the same sine of the double angle, so 45° and 45° pair, and 60° pairs with 30°.

Question 28Physics

A force of 10 N acts on a body and produces a displacement of 5 m. The angle between the force and the displacement is 60°. What is the work done by the force?

  1. 43.3 J
  2. 50 J
  3. 0 J
  4. 25 J Correct answer.

Explanation

Work is the dot product W = F·s·cosθ. Here W = 10 × 5 × cos60° = 50 × 0.5 = 25 J, so only the component of force along the displacement does work.

Question 29Physics

A body of mass 2 kg moving at 6 m/s collides head-on with a stationary body of mass 4 kg. If the collision is perfectly elastic, what is the velocity of the 2 kg body after the collision?

  1. 6 m/s in the original direction
  2. 0 m/s
  3. 2 m/s in the original direction
  4. −2 m/s, i.e. reversed Correct answer.

Explanation

For a 1-D elastic collision with a stationary target, v₁' = ((m₁ − m₂)/(m₁ + m₂))u₁. Substituting gives (2 − 4)/6 × 6 = −2 m/s, so the lighter body rebounds.

Question 30Physics

A body of weight 50 N rests on a horizontal surface. The coefficient of static friction is 0.4. What minimum horizontal force is needed to just start motion?

  1. 125 N
  2. 50 N
  3. 20 N Correct answer.
  4. 0 N

Explanation

Limiting static friction equals μs times the normal reaction, which here equals the weight on a horizontal surface. Thus f = 0.4 × 50 = 20 N, the minimum applied force to initiate sliding.

Question 31Physics

A wheel starting from rest attains an angular velocity of 20 rad/s in 4 s with uniform angular acceleration. Through what angle does it rotate in this time?

  1. 40 rad Correct answer.
  2. 80 rad
  3. 160 rad
  4. 20 rad

Explanation

For uniform angular acceleration from rest, θ = ½(ω₀ + ω)t = ½ × 20 × 4 = 40 rad. Equivalently, α = 5 rad/s² and θ = ½αt² = 40 rad.

Question 32Physics

A body of mass 2 kg is at rest at a height of 5 m above the ground. Taking g = 10 m/s², what is its total mechanical energy relative to the ground?

  1. 50 J
  2. 0 J
  3. 200 J
  4. 100 J Correct answer.

Explanation

At rest, kinetic energy is zero, so total mechanical energy equals potential energy mgh = 2 × 10 × 5 = 100 J. Mechanical energy is conserved during free fall, so this value stays constant.

Question 33Physics

Escape velocity from the surface of the Earth is about 11.2 km/s. What is the escape velocity from a planet whose mass and radius are both twice those of the Earth?

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

Explanation

Escape velocity is v = √(2GM/R). Doubling both M and R leaves the ratio M/R unchanged, so v stays the same at 11.2 km/s.

Question 34Physics

A body of mass 3 kg is attached to a string and whirled in a vertical circle of radius 2 m at constant speed 4 m/s. What is the tension in the string at the lowest point? (g = 10 m/s²)

  1. 30 N
  2. 24 N
  3. 54 N Correct answer.
  4. 6 N

Explanation

At the lowest point, tension acts upward and weight downward, so T − mg = mv²/r. Then T = mg + mv²/r = 30 + 3×16/2 = 30 + 24 = 54 N.

Question 35Physics

The bulk modulus of a liquid is 2 × 10⁹ Pa. What fractional decrease in volume occurs when the pressure is increased by 2 × 10⁵ Pa?

  1. 2 × 10⁻⁴
  2. 10⁻³
  3. 10⁻⁴ Correct answer.
  4. 10⁻²

Explanation

Bulk modulus B = −ΔP/(ΔV/V), so the fractional change is ΔP/B = 2×10⁵ / 2×10⁹ = 10⁻⁴. The negative sign only indicates the volume decreases.

Question 36Physics

A capillary tube of radius r is dipped in water. If a tube of radius r/2 is used instead, the height to which water rises changes by what factor?

  1. Quadrupled
  2. Unchanged
  3. Doubled Correct answer.
  4. Halved

Explanation

Capillary rise is h = 2T cosθ/(rρg), so h is inversely proportional to radius. Halving the radius therefore doubles the rise height.

Question 37Physics

An ideal gas is taken from state A to state B by two different paths. Which quantity is the same for both paths?

  1. Heat plus work done
  2. Change in internal energy Correct answer.
  3. Heat absorbed
  4. Work done by the gas

Explanation

Internal energy is a state function, so its change depends only on the initial and final states. Heat and work are path-dependent, but their difference Q − W is fixed by the state change.

Question 38Physics

A Carnot engine operates between 500 K and 300 K. What is its efficiency?

  1. 60%
  2. 40% Correct answer.
  3. 80%
  4. 20%

Explanation

Carnot efficiency is η = 1 − T_c/T_h, with temperatures in kelvin. Thus η = 1 − 300/500 = 0.40, i.e. 40%.

Question 39Physics

A gas at constant temperature has its volume doubled. Compared with the initial state, the pressure is:

  1. Halved Correct answer.
  2. Unchanged
  3. Doubled
  4. Quadrupled

Explanation

Boyle's law states that pV is constant at fixed temperature, so p is inversely proportional to V. Doubling the volume therefore halves the pressure.

Question 40Physics

A wave of frequency 50 Hz travels along a string with speed 200 m/s. What is the distance between two consecutive points on the string that are in the same phase?

  1. 4 m Correct answer.
  2. 8 m
  3. 2 m
  4. 0.25 m

Explanation

The distance between consecutive points in the same phase is the wavelength λ = v/f = 200/50 = 4 m. Adjacent in-phase points are separated by one full wavelength.

Question 41Physics

In a stationary wave on a string fixed at both ends, the distance between two adjacent nodes is 15 cm. What is the wavelength of the component waves?

  1. 60 cm
  2. 30 cm Correct answer.
  3. 7.5 cm
  4. 15 cm

Explanation

Adjacent nodes are separated by half a wavelength. So λ/2 = 15 cm, giving λ = 30 cm for the two travelling waves whose superposition forms the stationary wave.

Question 42Physics

An observer hears a sound of frequency 500 Hz from a source at rest. If the observer moves away from the source, the observed frequency will be:

  1. More than 500 Hz
  2. Exactly 500 Hz
  3. Exactly zero
  4. Less than 500 Hz Correct answer.

Explanation

When the observer recedes from a stationary source, fewer wavefronts reach the observer per second, so the observed frequency falls below the emitted frequency. The Doppler formula gives f' = f(v − v_o)/v.

Question 43Physics

Two identical point charges of +2 μC are placed 30 cm apart in vacuum. What is the magnitude of the force between them? (k = 9 × 10⁹ N·m²/C²)

  1. 0.04 N
  2. 40 N
  3. 0.4 N Correct answer.
  4. 4 N

Explanation

Coulomb's law gives F = kq₁q₂/r² = 9×10⁹ × (2×10⁻⁶)² / (0.3)². This equals 9×10⁹ × 4×10⁻¹² / 0.09 = 0.4 N.

Question 44Physics

A cell of emf 12 V and internal resistance 1 Ω is connected to an external resistance of 5 Ω. What is the terminal potential difference across the cell?

  1. 10 V Correct answer.
  2. 7 V
  3. 12 V
  4. 2 V

Explanation

The current is I = E/(R + r) = 12/6 = 2 A. The terminal voltage is V = E − Ir = 12 − 2×1 = 10 V, which is also IR = 2×5.

Question 45Physics

A wire of resistance R is stretched uniformly so that its length is doubled. Assuming volume stays constant, what is its new resistance?

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

Explanation

Stretching to double the length halves the cross-sectional area, since volume is fixed. Resistance R = ρL/A then becomes ρ(2L)/(A/2) = 4R.

Question 46Physics

A galvanometer of resistance 5 Ω gives full-scale deflection at 1 mA. What shunt resistance is needed to convert it into an ammeter of range 1 A?

  1. About 5 Ω
  2. About 50 Ω
  3. About 0.5 Ω
  4. About 0.005 Ω Correct answer.

Explanation

The shunt carries the excess current 1 − 0.001 ≈ 0.999 A while the galvanometer carries 0.001 A. Equal voltage gives S = (Ig × G)/(I − Ig) = (0.001 × 5)/0.999 ≈ 0.005 Ω.

Question 47Physics

A charged particle moves in a circular path in a uniform magnetic field. If its speed is doubled while the field stays the same, the radius of the path:

  1. Halves
  2. Becomes four times larger
  3. Doubles Correct answer.
  4. Remains the same

Explanation

The magnetic force provides the centripetal force, so qvB = mv²/r and r = mv/(qB). Radius is directly proportional to speed, so doubling v doubles r.

Question 48Physics

In a series LCR circuit at resonance, which statement is correct?

  1. The reactance of the inductor equals zero
  2. The impedance equals the resistance and current is maximum Correct answer.
  3. The current and voltage are 90° out of phase
  4. The impedance is zero and current is infinite

Explanation

At resonance the inductive and capacitive reactances are equal and cancel, so the net reactance is zero. The impedance is then purely resistive, equal to R, and the current reaches its maximum value.

Question 49Physics

Light of wavelength 600 nm in air enters a medium of refractive index 1.5. What is its wavelength inside the medium?

  1. 300 nm
  2. 400 nm Correct answer.
  3. 900 nm
  4. 600 nm

Explanation

Frequency is unchanged when light enters a medium, so wavelength scales as λ/n. Thus λ' = 600/1.5 = 400 nm inside the medium.

Question 50Physics

In Young's double-slit experiment, the fringe width is β. If the separation between the slits is doubled while the wavelength and screen distance are unchanged, the new fringe width is:

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

Explanation

Fringe width is β = λD/d, so it is inversely proportional to slit separation. Doubling d therefore halves the fringe width to β/2.