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Question 1Physics

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

  1. 30 m/s²
  2. 20 m/s²
  3. 7.5 m/s²
  4. 5 m/s² Correct answer.

Explanation

For uniform acceleration, a = (v − u)/t. Substituting gives (25 − 5)/4 = 20/4 = 5 m/s². The acceleration is positive because the velocity increases.

Question 2Physics

A projectile is launched at an angle θ to the horizontal with speed u, neglecting air resistance. At the highest point of its path, what is the magnitude of its acceleration?

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

Explanation

Throughout the flight, the only force on the projectile is gravity, so the acceleration is g directed vertically downward. At the top the vertical velocity is momentarily zero, but the acceleration is unchanged. The horizontal velocity is constant, so there is no horizontal acceleration.

Question 3Physics

A block of mass 2 kg rests on a horizontal surface with coefficient of static friction 0.4 (g = 10 m/s²). A horizontal force of 6 N is applied. What is the friction force acting on the block?

  1. 8 N
  2. 2 N
  3. 0 N
  4. 6 N Correct answer.

Explanation

The limiting static friction is μmg = 0.4 × 2 × 10 = 8 N. Since the applied force of 6 N is below this limit, the block does not move and static friction balances the applied force exactly, so it equals 6 N.

Question 4Physics

A car of mass 1000 kg rounds a flat circular curve of radius 50 m at 10 m/s. What is the minimum coefficient of static friction needed to prevent skidding?

  1. 1.0
  2. 0.5
  3. 0.1
  4. 0.2 Correct answer.

Explanation

On a flat curve, friction provides the centripetal force: μmg = mv²/r, so μ = v²/(rg) = 100/(50 × 10) = 0.2. The mass cancels out, so it does not affect the answer.

Question 5Physics

Two bodies of masses m and 2m are connected by a light string over a frictionless pulley. What is the acceleration of the system (g = 10 m/s²)?

  1. 5 m/s²
  2. 10/3 m/s² Correct answer.
  3. 20/3 m/s²
  4. 10 m/s²

Explanation

For an Atwood machine, a = (m₂ − m₁)g/(m₁ + m₂) = (2m − m)g/(3m) = g/3. With g = 10 m/s², the acceleration is 10/3 m/s². The tension is the same on both sides and the masses share one acceleration magnitude.

Question 6Physics

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

  1. 0.5 m/s
  2. 1 m/s Correct answer.
  3. 3 m/s
  4. 2 m/s

Explanation

In a perfectly inelastic collision, momentum is conserved: (2 × 3) = (2 + 4)v, so v = 6/6 = 1 m/s. Kinetic energy is not conserved, but momentum is.

Question 7Physics

A force F = (3i + 4j) N displaces a particle from the origin to a point (2i + 3j) m. What is the work done by the force?

  1. 17 J
  2. 18 J Correct answer.
  3. 7 J
  4. 12 J

Explanation

Work is the dot product W = F · d = (3)(2) + (4)(3) = 6 + 12 = 18 J. Only the component of force along the displacement does work.

Question 8Physics

A spring of force constant 200 N/m is compressed by 0.1 m. What elastic potential energy does it store?

  1. 1 J Correct answer.
  2. 20 J
  3. 2 J
  4. 0.5 J

Explanation

Elastic potential energy is U = ½kx² = ½ × 200 × (0.1)² = ½ × 200 × 0.01 = 1 J. The compression is squared, so halving the compression quarters the stored energy.

Question 9Physics

A body of mass 2 kg is raised vertically through 5 m at constant velocity (g = 10 m/s²). What is the work done by the applied force?

  1. 10 J
  2. 20 J
  3. 50 J
  4. 100 J Correct answer.

Explanation

At constant velocity the applied force equals the weight mg = 20 N, and work is force times displacement: 20 × 5 = 100 J. This work appears as an increase in gravitational potential energy.

Question 10Physics

A flywheel of moment of inertia 2 kg·m² rotates at 10 rad/s. What is its rotational kinetic energy?

  1. 20 J
  2. 100 J Correct answer.
  3. 200 J
  4. 50 J

Explanation

Rotational kinetic energy is ½Iω² = ½ × 2 × (10)² = 100 J. The angular velocity is squared, so doubling ω quadruples the energy.

Question 11Physics

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

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

Explanation

Rolling acceleration is a = g sin θ/(1 + I/mR²). The solid sphere has I/mR² = 2/5, smaller than the hollow cylinder's value of 1, so it accelerates more and arrives first. The result is independent of mass and incline angle.

Question 12Physics

Escape velocity from the surface of a planet is v. If a planet has the same density but twice the radius, what is its escape velocity?

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

Explanation

Escape velocity is v = √(2GM/R). With uniform density, M ∝ R³, so v ∝ √(R³/R) = R. Doubling the radius therefore doubles the escape velocity.

Question 13Physics

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

  1. 8 times the original Correct answer.
  2. 16 times the original
  3. 4 times the original
  4. 2 times the original

Explanation

Kepler's third law gives T² ∝ r³, so T ∝ r^(3/2). For r increased by a factor of 4, T increases by 4^(3/2) = 8.

Question 14Physics

A wire of length L and cross-sectional area A stretches by ΔL under a load. A second wire of the same material has length 2L and area 2A under the same load. Its extension is

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

Explanation

Extension is ΔL = FL/(AY). Doubling both L and A leaves the ratio L/A unchanged, so the extension stays ΔL. The Young's modulus is the same because the material is unchanged.

Question 15Physics

Water flows through a horizontal pipe whose cross-section narrows to half its original area. If the speed in the wider section is 2 m/s, the speed in the narrow section is

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

Explanation

By the equation of continuity, A₁v₁ = A₂v₂. Halving the area doubles the speed, so v₂ = 4 m/s. For an incompressible fluid in a horizontal pipe, the pressure falls where the speed rises.

Question 16Physics

A body of mass 0.5 kg is attached to a spring of constant 50 N/m and displaced 0.1 m from equilibrium. What is its angular frequency of oscillation?

  1. 10 rad/s Correct answer.
  2. 0.1 rad/s
  3. 100 rad/s
  4. 5 rad/s

Explanation

Angular frequency is ω = √(k/m) = √(50/0.5) = √100 = 10 rad/s. The amplitude does not affect the frequency for a simple harmonic oscillator.

Question 17Physics

A simple pendulum has period T on Earth. On a planet where the acceleration due to gravity is one quarter of that on Earth, its period becomes

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

Explanation

The period of a simple pendulum is T = 2π√(L/g). Reducing g to one quarter increases √(1/g) by a factor of 2, so the period becomes 2T.

Question 18Physics

Two identical sound sources emit waves in phase at the same frequency. At a point where the path difference is half a wavelength, the intensity is

  1. Maximum
  2. Half the maximum
  3. Zero Correct answer.
  4. One quarter of the maximum

Explanation

A path difference of λ/2 corresponds to a phase difference of π, giving destructive interference. Identical in-phase sources then cancel completely, so the intensity is zero at that point.

Question 19Physics

A wave travels along a stretched string. If the tension is quadrupled while the linear mass density is unchanged, the wave speed becomes

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

Explanation

String wave speed is v = √(T/μ). Quadrupling the tension multiplies the speed by √4 = 2. The density is unchanged, so only the tension ratio matters.

Question 20Physics

The absolute temperature of an ideal gas is doubled at constant volume. The root-mean-square speed of its molecules becomes

  1. √2 times the original Correct answer.
  2. Unchanged
  3. 2 times the original
  4. 4 times the original

Explanation

The rms speed is v_rms = √(3RT/M), so it is proportional to √T. Doubling the absolute temperature multiplies the speed by √2.

Question 21Physics

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

  1. Its temperature rises as volume increases
  2. It absorbs heat and does work Correct answer.
  3. It releases heat and does no work
  4. Its internal energy increases

Explanation

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

Question 22Physics

A Carnot engine operates between reservoirs at 600 K and 300 K. What is its efficiency?

  1. 50% Correct answer.
  2. 75%
  3. 25%
  4. 100%

Explanation

Carnot efficiency is η = 1 − T_c/T_h = 1 − 300/600 = 0.5, or 50%. The temperatures must be in kelvin, and no engine operating between these reservoirs can exceed this value.

Question 23Physics

Two point charges of +2 μC and −2 μC are separated by 0.1 m in vacuum. What is the magnitude of the force between them (k = 9 × 10⁹ N·m²/C²)?

  1. 3.6 N Correct answer.
  2. 1.8 N
  3. 7.2 N
  4. 36 N

Explanation

Coulomb's law gives F = kq₁q₂/r² = 9 × 10⁹ × (2 × 10⁻⁶ × 2 × 10⁻⁶)/(0.1)² = 9 × 10⁹ × 4 × 10⁻¹²/0.01 = 3.6 N. The opposite signs mean the force is attractive.

Question 24Physics

Three resistors of 3 Ω, 6 Ω and 9 Ω are connected in parallel. What is the equivalent resistance?

  1. 2 Ω
  2. 18 Ω
  3. 1.64 Ω Correct answer.
  4. 0.5 Ω

Explanation

For parallel resistors, 1/R = 1/3 + 1/6 + 1/9 = 6/18 + 3/18 + 2/18 = 11/18, so R = 18/11 ≈ 1.64 Ω. The equivalent resistance is always less than the smallest individual resistor.

Question 25Physics

A charged particle enters a uniform magnetic field with its velocity perpendicular to the field. What is the path of the particle?

  1. A parabola
  2. A circle of constant speed Correct answer.
  3. A helix along the field
  4. A straight line along the field

Explanation

The magnetic force qv × B is perpendicular to the velocity, so it changes direction but not speed. With velocity perpendicular to a uniform field, the particle moves in a circle of radius mv/(qB).

Question 26Physics

A particle moves in a straight line with uniform acceleration. Its velocity increases from 5 m/s to 15 m/s in 4 s. What is the acceleration of the particle?

  1. 5 m/s²
  2. 2 m/s²
  3. 2.5 m/s² Correct answer.
  4. 10 m/s²

Explanation

Acceleration is the rate of change of velocity, a = (v − u)/t. Substituting gives (15 − 5)/4 = 10/4 = 2.5 m/s².

Question 27Physics

A projectile is launched with speed u at an angle θ to the horizontal on level ground, with air resistance neglected. At the highest point of its path, what is the magnitude of its acceleration?

  1. g cos θ, directed along the path
  2. g sin θ, directed horizontally
  3. g, directed vertically downward Correct answer.
  4. Zero, since the vertical velocity is momentarily zero

Explanation

Throughout projectile motion the only force acting is gravity, so the acceleration is constant at g directed vertically downward. At the top the vertical velocity is zero but the acceleration is unchanged.

Question 28Physics

A block slides down a rough inclined plane of angle 30° at constant velocity. What is the coefficient of kinetic friction between the block and the plane?

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

Explanation

At constant velocity the net force along the incline is zero, so mg sin θ = μ mg cos θ, giving μ = tan θ. With θ = 30°, μ = tan 30° = 1/√3 ≈ 0.577.

Question 29Physics

A particle of mass m moves in a circle of radius r with constant speed v. Which expression gives the centripetal force acting on it?

  1. mr²/v
  2. mvr
  3. mv/r²
  4. mv²/r Correct answer.

Explanation

The centripetal force required to keep a body in circular motion is F = mv²/r, directed toward the centre. It follows from the centripetal acceleration v²/r multiplied by the mass.

Question 30Physics

A body of weight 50 N hangs from a light rope. A horizontal force is applied to the body so that the rope makes an angle of 45° with the vertical while the body stays in equilibrium. What is the magnitude of the horizontal force?

  1. 100 N
  2. 50 N Correct answer.
  3. 50√2 N
  4. 25 N

Explanation

Resolving forces, the horizontal applied force equals the horizontal component of the tension, and the vertical component balances the weight. Since T cos 45° = 50 N and T sin 45° = F, dividing gives F = 50 tan 45° = 50 N.

Question 31Physics

A body of mass 2 kg experiences a constant force of 8 N for 3 s starting from rest. What is the change in its momentum?

  1. 8 kg·m/s
  2. 12 kg·m/s
  3. 24 kg·m/s Correct answer.
  4. 48 kg·m/s

Explanation

By the impulse–momentum theorem, the change in momentum equals the impulse, F × t = 8 × 3 = 24 kg·m/s. The mass is not needed because the force and time are given directly.

Question 32Physics

A uniform metre stick is pivoted at its centre and is in equilibrium. A 10 g mass is hung 30 cm to the left of the pivot. Where must a 15 g mass be hung on the right side to balance it?

  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 the moments about the pivot must be equal: 10 × 30 = 15 × x. Solving gives x = 300/15 = 20 cm from the pivot.

Question 33Physics

A particle moves under a conservative force field. Which statement about its mechanical energy is correct?

  1. The potential energy remains constant throughout the motion
  2. The total mechanical energy always increases with time
  3. The total mechanical energy remains constant throughout the motion Correct answer.
  4. The kinetic energy remains constant throughout the motion

Explanation

For a conservative force, the work done depends only on position, so kinetic and potential energy interchange while their sum stays constant. Only the total, not the individual components, is conserved.

Question 34Physics

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

  1. 2 m/s in the original direction
  2. 1 m/s in the original direction Correct answer.
  3. 1.5 m/s in the original direction
  4. 0.5 m/s in the original direction

Explanation

Momentum is conserved in a perfectly inelastic collision: (2 × 3) = (2 + 4) × v. Solving gives v = 6/6 = 1 m/s in the original direction.

Question 35Physics

A wheel of radius 0.5 m rolls without slipping along a horizontal road. Its centre moves at 4 m/s. What is the angular velocity of the wheel?

  1. 8 rad/s Correct answer.
  2. 2 rad/s
  3. 0.125 rad/s
  4. 4 rad/s

Explanation

For rolling without slipping the centre speed equals ωr, so ω = v/r = 4/0.5 = 8 rad/s.

Question 36Physics

A body weighs 60 N on the surface of Earth. At a height above the surface equal to Earth's radius, what is its weight?

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

Explanation

Weight varies as 1/r² from Earth's centre. At height R above the surface the distance from the centre is 2R, so the weight becomes 60/2² = 15 N.

Question 37Physics

A steel wire of cross-sectional area 2 × 10⁻⁶ m² is stretched by a force of 100 N. What is the tensile stress in the wire?

  1. 5 × 10⁷ N/m² Correct answer.
  2. 2 × 10⁸ N/m²
  3. 2 × 10⁻⁴ N/m²
  4. 5 × 10⁴ N/m²

Explanation

Tensile stress is force per unit area: 100/(2 × 10⁻⁶) = 5 × 10⁷ N/m².

Question 38Physics

A liquid rises to a height h in a capillary tube of radius r. In a tube of the same material but radius r/2, the liquid rises to a height

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

Explanation

Capillary rise is inversely proportional to the tube radius, h ∝ 1/r, for the same liquid and material. Halving the radius therefore doubles the rise to 2h.

Question 39Physics

Water flows through a horizontal pipe whose cross-section narrows to half its original area. If the speed in the wider section is 2 m/s, what is the speed in the narrower section?

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

Explanation

By the equation of continuity, Av = constant, so halving the area doubles the speed. The speed in the narrow section is therefore 4 m/s.

Question 40Physics

A body of mass 0.5 kg attached to a spring of constant 50 N/m is displaced 0.1 m from equilibrium and released. What is its maximum speed?

  1. 10 m/s
  2. 1 m/s Correct answer.
  3. 2 m/s
  4. 0.5 m/s

Explanation

For simple harmonic motion the maximum speed is v_max = ωA, with ω = √(k/m) = √(50/0.5) = 10 rad/s. Thus v_max = 10 × 0.1 = 1 m/s.

Question 41Physics

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

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

Explanation

The period of a simple pendulum is T = 2π√(L/g), so T ∝ 1/√g. Reducing g to one quarter multiplies T by 2, giving 4 s.

Question 42Physics

Two identical sound sources emit waves in phase at the same frequency. At a point where the path difference is half a wavelength, the interference is

  1. neither, since the sources are identical
  2. constructive, with maximum intensity
  3. constructive only if the amplitudes differ
  4. destructive, with minimum intensity Correct answer.

Explanation

A path difference of half a wavelength corresponds to a phase difference of π, so the waves arrive in antiphase and interfere destructively. The resultant intensity is a minimum at that point.

Question 43Physics

A wave travels along a stretched string. If the tension is increased to four times its original value with the linear mass density unchanged, the wave speed becomes

  1. 4 times the original
  2. 16 times the original
  3. half the original
  4. 2 times the original Correct answer.

Explanation

The speed of a transverse wave on a string is v = √(T/μ), so v ∝ √T. Quadrupling the tension multiplies the speed by √4 = 2.

Question 44Physics

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

  1. The internal energy stays constant and the gas absorbs heat equal to the work done Correct answer.
  2. The internal energy increases and no heat is exchanged
  3. The gas does no work because the temperature is constant
  4. The internal energy decreases and heat is released

Explanation

For an ideal gas the internal energy depends only on temperature, so it is unchanged in an isothermal process. By the first law, Q = W, meaning the heat absorbed equals the work done by the gas.

Question 45Physics

Equal fixed charges +q are at (a,0) and (0,a), where a>0. A test charge +Q is at the origin. Let F=kqQ/a². What is the net force on +Q?

  1. Zero
  2. F i + F j
  3. -F i - F j Correct answer.
  4. -2F i

Explanation

Each positive source repels the positive test charge. The charge on the positive x-axis contributes -F i, and the other contributes -F j, so their vector sum is -F i-F j.

Question 46Physics

Three resistors of 3 Ω, 6 Ω and 9 Ω are connected in parallel. What is the equivalent resistance of the combination?

  1. 11/18 Ω
  2. 18/11 Ω Correct answer.
  3. 2 Ω
  4. 18 Ω

Explanation

For parallel resistors, 1/R = 1/3 + 1/6 + 1/9 = 6/18 + 3/18 + 2/18 = 11/18, so R = 18/11 Ω ≈ 1.64 Ω.

Question 47Physics

A parallel-plate capacitor has plate area A and separation d. A dielectric slab of dielectric constant K completely fills the space between its plates. Which expression gives the new capacitance?

  1. ε₀A/d
  2. Kε₀A/d Correct answer.
  3. ε₀A/(Kd)
  4. Kε₀A/d²

Explanation

Inserting a dielectric of constant K multiplies the vacuum capacitance C₀ = ε₀A/d by K, because the induced bound charges reduce the effective field between the plates for the same free charge. Hence C = Kε₀A/d, which is larger than the air-filled value.

Question 48Physics

A galvanometer of resistance 50 Ω gives full-scale deflection for a current of 1 mA. It is to be converted into a voltmeter reading up to 10 V. What series resistance is required?

  1. 50 Ω
  2. 9950 Ω Correct answer.
  3. 10000 Ω
  4. 995 Ω

Explanation

For a voltmeter the multiplier resistance R is placed in series so that full-scale current flows when the total voltage is 10 V. The total circuit resistance must be V/I = 10/(1×10⁻³) = 10000 Ω, and subtracting the galvanometer's own 50 Ω gives R = 9950 Ω.

Question 49Physics

Light of wavelength 500 nm in vacuum passes from air into glass of refractive index 1.5. Which statement about the light in the glass is correct?

  1. Its speed and its frequency both increase by a factor of 1.5.
  2. Its wavelength stays the same while its frequency decreases by a factor of 1.5.
  3. Both its wavelength and its frequency decrease by a factor of 1.5.
  4. Its frequency stays the same while its wavelength becomes about 333 nm. Correct answer.

Explanation

The frequency of a wave is fixed by the source and does not change when light crosses a boundary, whereas the speed falls to v = c/n and the wavelength scales as λ/n. Thus λ_glass = 500/1.5 ≈ 333 nm with the frequency unchanged.

Question 50Physics

In a Young's double-slit experiment the fringe width is β. The source wavelength is halved and the slit separation is doubled, with the screen distance unchanged. What is the new fringe width?

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

Explanation

Fringe width is β = λD/d, so it is directly proportional to wavelength and inversely proportional to slit separation. Halving λ gives β/2, and doubling d then gives β/4.