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SRMHCAT practice questions

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Question 1Physics

A body moves along a straight line with constant acceleration. Its velocity increases from 5 m/s to 15 m/s in 4 s. What distance does it cover in this interval?

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

Explanation

For uniform acceleration the average velocity is the mean of initial and final velocities, (5+15)/2 = 10 m/s. Multiplying by the 4 s interval gives 40 m. Equivalently, acceleration is 2.5 m/s² and s = ut + ½at² = 20 + 20 = 40 m.

Question 2Physics

Which quantity remains constant for a projectile in flight when air resistance is neglected?

  1. Kinetic energy
  2. Speed
  3. Horizontal component of velocity Correct answer.
  4. Vertical component of velocity

Explanation

With no air resistance there is no horizontal force, so the horizontal velocity component is unchanged throughout the flight. Gravity acts vertically, so the vertical component, the speed and the kinetic energy all vary with height.

Question 3Physics

A force of 20 N acts on a 4 kg body initially at rest on a frictionless surface. What is the body's speed after 3 s?

  1. 60 m/s
  2. 15 m/s Correct answer.
  3. 12 m/s
  4. 5 m/s

Explanation

Newton's second law gives acceleration a = F/m = 20/4 = 5 m/s². With zero initial velocity, v = at = 5 × 3 = 15 m/s.

Question 4Physics

Two bodies of masses m and 2m have equal kinetic energies. What is the ratio of their momenta?

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

Explanation

Kinetic energy can be written K = p²/2m, so p = √(2mK). For equal K, momentum is proportional to √m, giving p₁ : p₂ = √m : √(2m) = 1 : √2.

Question 5Physics

A wheel starting from rest reaches an angular speed of 20 rad/s in 4 s with uniform angular acceleration. What is the angular acceleration?

  1. 2.5 rad/s²
  2. 5 rad/s² Correct answer.
  3. 0.2 rad/s²
  4. 80 rad/s²

Explanation

For uniform angular acceleration, α = Δω/Δt = (20 − 0)/4 = 5 rad/s². The angular displacement in this time would be ½αt² = 40 rad.

Question 6Physics

A solid sphere and a hollow spherical shell 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 incline angle
  2. Both arrive together
  3. The hollow shell
  4. The solid sphere Correct answer.

Explanation

Rolling acceleration is a = g sinθ/(1 + I/mR²). The solid sphere has I/mR² = 2/5 while the shell has 2/3, so the sphere has the larger acceleration and arrives first. The result is independent of the incline angle.

Question 7Physics

The gravitational field strength at the surface of a planet is g. At a height equal to the planet's radius above the surface, the field strength is:

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

Explanation

Field strength follows an inverse-square law, g = GM/r². At height equal to the radius, the distance from the centre doubles, so the field becomes g/2² = g/4.

Question 8Physics

A body of mass 2 kg moving at 6 m/s collides head-on with a stationary 4 kg body and they stick together. What is the speed of the combined mass?

  1. 3 m/s
  2. 2 m/s Correct answer.
  3. 1 m/s
  4. 6 m/s

Explanation

Momentum is conserved in a perfectly inelastic collision: 2 × 6 = (2 + 4) × v. Solving gives v = 12/6 = 2 m/s. Kinetic energy is not conserved, being lost to deformation and heat.

Question 9Physics

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

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

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 each form holds half the total energy.

Question 10Physics

Which of the following is a necessary condition for a body to be in stable equilibrium?

  1. Its weight is balanced by an equal upward force at the same point
  2. Its centre of gravity is at its lowest possible position Correct answer.
  3. Its centre of gravity is at its highest possible position
  4. The net force on it is zero but the net torque is nonzero

Explanation

In stable equilibrium a small displacement raises the centre of gravity, producing a restoring torque that returns the body. The lowest centre-of-gravity position therefore characterises stability, while neutral and unstable states differ.

Question 11Physics

Water flows through a horizontal pipe whose cross-sectional area halves along the flow. What happens to the pressure in the narrower section?

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

Explanation

Continuity requires Av to be constant, so halving the area doubles the speed. Bernoulli's equation then requires the pressure to fall where the speed rises, since the pipe is horizontal.

Question 12Physics

A block of volume 2 × 10⁻⁴ m³ floats with half its volume submerged in water of density 1000 kg/m³. What is the block's weight?

  1. 0.5 N
  2. 4 N
  3. 2 N
  4. 1 N Correct answer.

Explanation

The buoyant force equals the weight of displaced water: ρV_submerged g = 1000 × 1 × 10⁻⁴ × 10 = 1 N. For floating, weight equals buoyancy, so the block weighs 1 N.

Question 13Physics

An ideal gas is compressed isothermally to half its volume. What happens to its pressure?

  1. It doubles Correct answer.
  2. It becomes four times larger
  3. It stays the same
  4. It halves

Explanation

Boyle's law states that at constant temperature pV is constant. Halving the volume therefore doubles the pressure, since the same number of molecules strikes a smaller area more frequently.

Question 14Physics

Two rods of the same material and length have cross-sectional areas A and 2A. If the thinner rod has thermal resistance R, what is the resistance of the thicker rod?

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

Explanation

Thermal resistance for conduction is R_th = L/(kA), inversely proportional to area. Doubling the area halves the resistance, giving R/2.

Question 15Physics

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

  1. 100%
  2. 25%
  3. 33%
  4. 50% Correct answer.

Explanation

The Carnot efficiency is 1 − T_cold/T_hot = 1 − 300/600 = 0.5, or 50%. No real engine between these reservoirs can exceed this value.

Question 16Physics

A particle of charge q moves with velocity v perpendicular to a uniform magnetic field B. The path followed is:

  1. A circle Correct answer.
  2. A straight line
  3. A helix
  4. A parabola

Explanation

The magnetic force qv × B is always perpendicular to the velocity, so it changes direction but not speed. A constant perpendicular force produces uniform circular motion with radius mv/(qB).

Question 17Physics

Three identical resistors of 6 Ω each are connected in parallel. What is the equivalent resistance?

  1. 2 Ω Correct answer.
  2. 3 Ω
  3. 18 Ω
  4. 6 Ω

Explanation

For n identical resistors in parallel, R_eq = R/n = 6/3 = 2 Ω. Equivalently, 1/R_eq = 1/6 + 1/6 + 1/6 = 1/2.

Question 18Physics

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

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

Explanation

Stretching to double length halves the cross-sectional area because volume is conserved. Resistance is ρL/A, so doubling L and halving A multiplies R by four.

Question 19Physics

A parallel-plate capacitor is charged and then disconnected from the battery. If the plate separation is doubled, the stored energy:

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

Explanation

With the battery removed, charge Q is fixed. Capacitance falls to C/2 when separation doubles, and energy U = Q²/2C therefore doubles. The work comes from the mechanical force needed to separate the plates.

Question 20Physics

Two coherent light waves of wavelength λ arrive at a point with a path difference of λ/2. The point shows:

  1. No interference
  2. Destructive interference Correct answer.
  3. A path difference equal to one wavelength
  4. Constructive interference

Explanation

A path difference of half a wavelength corresponds to a phase difference of π radians. The waves then arrive in antiphase and cancel, producing destructive interference.

Question 21Physics

The speed of sound in air is about 340 m/s. What is the wavelength of a 170 Hz sound wave in air?

  1. 0.5 m
  2. 2 m Correct answer.
  3. 5 m
  4. 0.2 m

Explanation

The wave relation v = fλ gives λ = v/f = 340/170 = 2 m. Frequency is set by the source while wavelength adjusts to the medium's speed.

Question 22Physics

A convex lens of focal length 10 cm forms an image of an object placed 15 cm in front of it. The image is:

  1. Real, inverted and magnified Correct answer.
  2. Virtual, erect and magnified
  3. Virtual, erect and diminished
  4. Real, inverted and diminished

Explanation

Using 1/f = 1/v − 1/u with u = −15 cm and f = 10 cm gives v = +30 cm, a real image. Magnification m = v/u = −2, so the image is inverted and twice as large.

Question 23Physics

Light travelling in glass of refractive index 1.5 enters air. What is the critical angle for total internal reflection?

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

Explanation

The critical angle satisfies sin C = n₂/n₁ = 1/1.5 = 0.667, giving C ≈ 42°. Beyond this angle the light is totally internally reflected.

Question 24Physics

In the photoelectric effect, increasing the intensity of incident light of fixed frequency above the threshold increases:

  1. The threshold frequency
  2. The work function of the metal
  3. The maximum kinetic energy of emitted electrons
  4. The number of photoelectrons emitted per second Correct answer.

Explanation

Each photon carries energy hf, so intensity sets the photon arrival rate and hence the emission rate. The maximum kinetic energy depends on frequency, and the work function is a property of the metal.

Question 25Physics

A radioactive sample has a half-life of 8 days. What fraction of the original nuclei remains after 24 days?

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

Explanation

24 days is three half-lives. Each half-life halves the remaining nuclei, so the fraction is (1/2)³ = 1/8.

Question 26Physics

A projectile is launched at 20 m/s at 30° above the horizontal on level ground. Taking g = 10 m/s², what is the maximum height reached?

  1. 2.5 m
  2. 20 m
  3. 5 m Correct answer.
  4. 10 m

Explanation

The vertical component of velocity is u sinθ = 20 × 0.5 = 10 m/s. Maximum height follows from H = u_y²/(2g) = 100/20 = 5 m. Horizontal motion plays no role in the vertical rise.

Question 27Physics

A body moves in a straight line with constant acceleration. Its velocity increases from 4 m/s to 12 m/s in 4 s. What distance does it cover in this interval?

  1. 48 m
  2. 32 m Correct answer.
  3. 16 m
  4. 64 m

Explanation

With constant acceleration the average velocity is (4 + 12)/2 = 8 m/s. Multiplying by the time gives s = 8 × 4 = 32 m. Equivalently, acceleration is 2 m/s² and s = ut + ½at² = 16 + 16 = 32 m.

Question 28Physics

A force of 10 N acts on a body of mass 5 kg initially at rest for 3 s. What is the body's final momentum?

  1. 50 kg m/s
  2. 30 kg m/s Correct answer.
  3. 15 kg m/s
  4. 6 kg m/s

Explanation

Impulse equals change in momentum: F × t = 10 × 3 = 30 kg m/s. Since the body starts from rest, this impulse is the final momentum. The mass is not needed once impulse is used.

Question 29Physics

A wheel starting from rest reaches an angular speed of 20 rad/s in 5 s with uniform angular acceleration. What is the angular acceleration?

  1. 100 rad/s²
  2. 4 rad/s² Correct answer.
  3. 2 rad/s²
  4. 5 rad/s²

Explanation

For uniform angular acceleration, α = (ω − ω₀)/t = (20 − 0)/5 = 4 rad/s². The angular displacement is not required because the speeds and time are given directly.

Question 30Physics

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

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

Explanation

Circular orbital speed satisfies v² = GM/r, so v is proportional to 1/√r. Increasing the radius therefore reduces the speed. A larger orbit is slower because the gravitational pull available at that distance is weaker.

Question 31Physics

A spring of force constant 200 N/m is compressed by 0.1 m. How much elastic potential energy is stored?

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

Explanation

Elastic potential energy is U = ½kx² = ½ × 200 × (0.1)² = 1 J. Squaring the compression is essential because the energy grows with the square of the deformation.

Question 32Physics

A wave has frequency 50 Hz and wavelength 4 m. What is its speed?

  1. 54 m/s
  2. 200 m/s Correct answer.
  3. 0.08 m/s
  4. 12.5 m/s

Explanation

Wave speed is the product of frequency and wavelength: v = fλ = 50 × 4 = 200 m/s. Frequency counts oscillations per second and wavelength gives the distance per oscillation.

Question 33Physics

Two point charges of +2 μC and +8 μC are separated by 0.3 m in vacuum. What is the magnitude of the electrostatic force between them? Take k = 9 × 10⁹ N m²/C².

  1. 160 N
  2. 1.6 N Correct answer.
  3. 4.8 N
  4. 16 N

Explanation

Coulomb's law gives F = kq₁q₂/r² = 9 × 10⁹ × 2 × 10⁻⁶ × 8 × 10⁻⁶ / 0.09. The numerator is 0.144 and dividing by 0.09 yields 1.6 N. Both charges are positive, so the force is repulsive.

Question 34Physics

A body of mass 3 kg is pulled along a rough horizontal floor by a horizontal force of 20 N. The friction force is 8 N. What is the acceleration of the body?

  1. 9.33 m/s²
  2. 2.67 m/s²
  3. 6.67 m/s²
  4. 4 m/s² Correct answer.

Explanation

The net horizontal force is 20 − 8 = 12 N. Newton's second law then gives a = F_net/m = 12/3 = 4 m/s². Friction must be subtracted because it opposes the applied force.

Question 35Physics

A 0.5 kg ball moving at 8 m/s strikes a wall perpendicularly and rebounds at 6 m/s. What is the magnitude of the change in momentum of the ball?

  1. 1 kg m/s
  2. 14 kg m/s
  3. 4 kg m/s
  4. 7 kg m/s Correct answer.

Explanation

Taking the initial direction as positive, initial momentum is +4 kg m/s and final momentum is −3 kg m/s. The change is −3 − 4 = −7 kg m/s, so the magnitude is 7 kg m/s. The reversal of direction is what makes the magnitudes add.

Question 36Physics

A uniform metre rule is pivoted at its centre. A 2 N weight hangs 30 cm to the left of the pivot. Where must a 3 N weight be placed on the right to balance the rule?

  1. 30 cm from the pivot
  2. 45 cm from the pivot
  3. 10 cm from the pivot
  4. 20 cm from the pivot Correct answer.

Explanation

For rotational equilibrium the moments must balance: 2 × 30 = 3 × d. Solving gives d = 60/3 = 20 cm from the pivot on the right. The rule's own weight acts at the pivot and contributes no moment.

Question 37Physics

A body of mass 2 kg is raised through 5 m and then allowed to fall freely. Taking g = 10 m/s², what is its speed just before hitting the ground?

  1. 5 m/s
  2. 10 m/s Correct answer.
  3. 50 m/s
  4. 20 m/s

Explanation

Equating potential energy lost to kinetic energy gained gives ½v² = gh, so v = √(2gh) = √(2 × 10 × 5) = 10 m/s. The mass cancels, so the answer is independent of the 2 kg value.

Question 38Physics

The moment of inertia of a disc about an axis through its centre and perpendicular to its plane is ½MR². What is its moment of inertia about a parallel axis through a point on its rim?

  1. 3/2 MR² Correct answer.
  2. MR²
  3. 2MR²
  4. ½MR²

Explanation

The parallel-axis theorem adds MR² to the centre-of-mass value: I = ½MR² + MR² = 3/2 MR². The distance from centre to rim is R, so the added term is exactly MR².

Question 39Physics

A body of mass 1 kg attached to a string of length 1 m moves in a vertical circle. At the lowest point its speed is 5 m/s. Taking g = 10 m/s², what is the tension in the string there?

  1. 50 N
  2. 35 N Correct answer.
  3. 25 N
  4. 15 N

Explanation

At the lowest point the tension acts upward and weight downward, giving T − mg = mv²/r. Thus T = mg + mv²/r = 10 + 25 = 35 N. Both terms are needed because the string supplies the centripetal force and supports the weight.

Question 40Physics

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

  1. Its temperature rises because no heat enters
  2. Its temperature stays constant because no heat is exchanged
  3. Its temperature falls because it does work at the expense of internal energy Correct answer.
  4. Its internal energy rises because the volume increases

Explanation

In an adiabatic process Q = 0, so the first law gives ΔU = −W. When the gas expands it does positive work, internal energy falls, and temperature drops. The absence of heat exchange does not mean temperature is constant.

Question 41Physics

A mixture contains 2 mol of a gas at 300 K and 3 mol of another gas at 400 K in the same rigid insulated container. What is the final equilibrium temperature?

  1. 350 K
  2. 330 K
  3. 360 K Correct answer.
  4. 340 K

Explanation

If the molar heat capacities are equal, energy conservation gives (2 × 300 + 3 × 400)/5 = (600 + 1200)/5 = 360 K. The final temperature is the mole-weighted average of the initial temperatures. Insulation ensures no energy leaves the container.

Question 42Physics

A charge of 5 μC is moved between two points whose potential difference is 200 V. How much work is done by the electric field?

  1. 2.5 × 10⁻⁸ J
  2. 1 × 10⁻³ J Correct answer.
  3. 1 × 10⁻⁶ J
  4. 4 × 10⁻⁴ J

Explanation

Work done by the field equals qΔV = 5 × 10⁻⁶ × 200 = 1 × 10⁻³ J. Potential difference is work per unit charge, so multiplying by the charge gives the energy.

Question 43Physics

A galvanometer of resistance 5 Ω gives full-scale deflection for 1 mA. What shunt resistance converts it into an ammeter reading up to 1 A?

  1. 5000 Ω
  2. 0.005 Ω Correct answer.
  3. 0.05 Ω
  4. 5 Ω

Explanation

The shunt carries the excess current 1 − 0.001 ≈ 0.999 A while the coil carries 0.001 A. Equal voltage gives S = (Ig × G)/(I − Ig) ≈ (0.001 × 5)/0.999 ≈ 0.005 Ω. A very small shunt is needed to divert almost all the current.

Question 44Physics

A charged particle enters a uniform magnetic field with its velocity parallel to the field lines. What is the magnetic force on it?

  1. Maximum, along the velocity
  2. Maximum, perpendicular to the velocity
  3. Half the maximum value
  4. Zero Correct answer.

Explanation

The magnetic force is F = qvB sinθ, where θ is the angle between velocity and field. When the velocity is parallel, θ = 0 and sinθ = 0, so the force vanishes. No magnetic work is done and the particle continues in a straight line.

Question 45Physics

In a step-down transformer with 1000 turns in the primary and 200 turns in the secondary, the primary is connected to 220 V AC. Assuming ideal coupling, what is the secondary voltage?

  1. 44 V Correct answer.
  2. 11 V
  3. 110 V
  4. 1100 V

Explanation

For an ideal transformer Vs/Vp = Ns/Np = 200/1000 = 0.2. Hence Vs = 0.2 × 220 = 44 V. A step-down transformer reduces voltage in the same ratio as the turns ratio.

Question 46Physics

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

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

Explanation

The pendulum period is T = 2π√(L/g), so period varies as 1/√g. If g falls to one quarter, √g falls to one half and the period doubles to 2T. The length and mass are unchanged.

Question 47Physics

An object is placed 10 cm from a concave mirror of focal length 15 cm. Where is the image formed?

  1. 30 cm in front of the mirror
  2. 30 cm behind the mirror Correct answer.
  3. 6 cm behind the mirror
  4. 6 cm in front of the mirror

Explanation

Using 1/f = 1/v + 1/u with sign convention u = −10 cm and f = −15 cm gives 1/v = −1/15 + 1/10 = 1/30, so v = +30 cm. A positive image distance for a concave mirror places the image behind the mirror, virtual and erect.

Question 48Physics

A double slit is illuminated with light of wavelength 600 nm and the third-order bright fringe is observed at an angle of 30°. What is the slit separation?

  1. 3.6 × 10⁻⁶ m Correct answer.
  2. 1.2 × 10⁻⁶ m
  3. 1.8 × 10⁻⁶ m
  4. 6.0 × 10⁻⁷ m

Explanation

Bright fringes obey d sinθ = nλ. With n = 3, λ = 600 nm and sin30° = 0.5, d = (3 × 600 × 10⁻⁹)/0.5 = 3.6 × 10⁻⁶ m. The sine of the angle, not the angle itself, enters the formula.

Question 49Physics

In a photoelectric experiment the stopping potential is 1.5 V for light of frequency f. If the frequency is doubled while the metal is unchanged, what is the new stopping potential? Take h/e = 4.14 × 10⁻¹⁵ V s and f = 1.0 × 10¹⁵ Hz.

  1. 4.14 V
  2. 7.14 V
  3. 3.0 V
  4. 5.64 V Correct answer.

Explanation

Einstein's equation gives hf = φ + eV₀. At f = 1 × 10¹⁵ Hz, hf/e = 4.14 V, so the work function is 4.14 − 1.5 = 2.64 V in electron-volt terms. At 2f the photon energy is 8.28 V, giving V₀ = 8.28 − 2.64 = 5.64 V.

Question 50Physics

A nucleus of mass number 240 undergoes alpha decay followed by two beta-minus decays. What are the mass number and atomic number of the final nucleus?

  1. 240 and 90
  2. 236 and 88
  3. 236 and 90 Correct answer.
  4. 236 and 92

Explanation

Alpha decay reduces mass number by 4 and atomic number by 2, giving 236 and Z − 2. Each beta-minus decay leaves the mass number unchanged but raises the atomic number by 1, so two raise it by 2. The net change is mass number 236 and atomic number unchanged from the original, here 90.