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Question 1Physics

A body starts from rest and moves with a uniform acceleration of 2 m/s². What distance does it cover in the first 5 s?

  1. 20 m
  2. 50 m
  3. 10 m
  4. 25 m Correct answer.

Explanation

For motion from rest with uniform acceleration, s = ut + ½at². Substituting u = 0, a = 2 m/s², and t = 5 s gives s = ½ × 2 × 25 = 25 m. The other values come from using an incorrect time dependence or omitting the factor ½.

Question 2Physics

The dimensional formula of impulse is identical to that of which physical quantity?

  1. Momentum Correct answer.
  2. Energy
  3. Force
  4. Power

Explanation

Impulse is force multiplied by the time interval, so its dimensions are [MLT⁻²][T] = [MLT⁻¹]. This is also the dimension of momentum, consistent with the impulse–momentum theorem, which states that impulse equals the change in momentum.

Question 3Physics

For an ideal gas undergoing an isothermal process, which quantity is zero?

  1. Change in internal energy Correct answer.
  2. Heat exchanged with the surroundings
  3. Change in pressure
  4. Work done by the gas

Explanation

The internal energy of an ideal gas depends only on its temperature. In an isothermal process the temperature remains constant, so ΔT = 0 and therefore ΔU = 0, while heat and work are generally nonzero.

Question 4Physics

A ball is projected from level ground at 45° to the horizontal with a speed of 20 m/s. Taking g = 10 m/s², what is its horizontal range?

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

Explanation

For projectile motion on level ground, the range is R = u² sin 2θ / g. With u = 20 m/s, θ = 45°, sin 90° = 1, and g = 10 m/s², R = 400/10 = 40 m.

Question 5Physics

A 6 Ω resistor and a 3 Ω resistor are connected in parallel across a 6 V battery of negligible internal resistance. What total current does the battery supply?

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

Explanation

For parallel resistors, 1/R = 1/6 + 1/3 = 1/2, so the equivalent resistance is 2 Ω. The total current is I = V/R = 6/2 = 3 A, which is also the sum of the branch currents 1 A and 2 A.

Question 6Physics

An object is placed 30 cm in front of a concave mirror of focal length 15 cm. What is the magnification produced by the mirror?

  1. +2
  2. +1
  3. −1 Correct answer.
  4. −0.5

Explanation

Using the mirror formula 1/v + 1/u = 1/f with u = −30 cm and f = −15 cm gives v = −30 cm. The magnification is m = −v/u = −(−30)/(−30) = −1, so the image is real, inverted, and the same size as the object.

Question 7Physics

A long straight wire carries a current of 5 A. Taking μ₀ = 4π × 10⁻⁷ T·m/A, what is the magnetic field at a distance of 0.1 m from the wire?

  1. 1 × 10⁻⁵ T Correct answer.
  2. 2 × 10⁻⁵ T
  3. 5 × 10⁻⁵ T
  4. 5 × 10⁻⁶ T

Explanation

The magnetic field of a long straight wire is B = μ₀I/(2πr). Substituting μ₀ = 4π × 10⁻⁷ T·m/A, I = 5 A, and r = 0.1 m gives B = (4π × 10⁻⁷ × 5)/(2π × 0.1) = 1 × 10⁻⁵ T.

Question 8Physics

A particle executes simple harmonic motion with amplitude 5 cm and time period 0.2 s. What is its maximum speed?

  1. 3.14 m/s
  2. 0.25 m/s
  3. 0.50 m/s
  4. 1.57 m/s Correct answer.

Explanation

In SHM the maximum speed is vₘₐₓ = ωA, where ω = 2π/T. Here T = 0.2 s, so ω = 2π/0.2 = 10π rad/s, and A = 0.05 m. Thus vₘₐₓ = 10π × 0.05 = 0.5π ≈ 1.57 m/s.

Question 9Physics

A solid sphere rolls without slipping on a horizontal surface. What fraction of its total kinetic energy is rotational kinetic energy?

  1. 2/5
  2. 1/3
  3. 5/7
  4. 2/7 Correct answer.

Explanation

For a solid sphere, I = (2/5)mr² and rolling means ω = v/r. The translational kinetic energy is ½mv², while the rotational kinetic energy is ½Iω² = (1/5)mv². The total is (7/10)mv², so the rotational fraction is (1/5)/(7/10) = 2/7.

Question 10Physics

A metal surface has a threshold wavelength of 500 nm. Light of wavelength 400 nm falls on it. Taking hc = 1240 eV·nm, what is the maximum kinetic energy of the emitted photoelectrons?

  1. 2.48 eV
  2. 0.62 eV Correct answer.
  3. 1.24 eV
  4. 0.31 eV

Explanation

The incident photon energy is hc/λ = 1240/400 = 3.10 eV, and the threshold energy is 1240/500 = 2.48 eV. By Einstein’s photoelectric equation, the maximum kinetic energy is 3.10 − 2.48 = 0.62 eV.

Question 11Physics

The dimensional formula of the universal gravitational constant G is which of the following?

  1. M⁻¹ L³ T⁻¹
  2. M⁻¹ L³ T⁻² Correct answer.
  3. M⁻¹ L² T⁻²
  4. M L³ T⁻²

Explanation

Newton's law of gravitation gives F = G m₁m₂ / r², so G = F r² / (m₁m₂). Substituting the dimensions of force, length and mass gives M L T⁻² × L² / M², which simplifies to M⁻¹ L³ T⁻².

Question 12Physics

For a particle moving along a straight line, the area under its velocity–time graph between two instants represents which quantity?

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

Explanation

Velocity is the rate of change of displacement, so integrating velocity with respect to time gives displacement: Δx = ∫v dt. Graphically, this integral is the area under the velocity–time graph.

Question 13Physics

A block of mass 2 kg is lifted vertically through a height of 3 m at constant speed. Taking g = 10 m/s², what is the work done by the applied force?

  1. 30 J
  2. 60 J Correct answer.
  3. 0 J
  4. 6 J

Explanation

Because the block moves at constant speed, the upward applied force balances its weight, so F = mg = 20 N. The work done by this force is F × distance = 20 N × 3 m = 60 J.

Question 14Physics

During an adiabatic expansion, an ideal gas does 40 J of work on its surroundings. What is the change in its internal energy?

  1. −40 J Correct answer.
  2. 0 J
  3. +40 J
  4. It depends on the pressure of the gas

Explanation

For an adiabatic process, Q = 0, and the first law gives ΔU = Q − W, where W is work done by the gas. Thus ΔU = 0 − 40 J = −40 J, so the internal energy decreases.

Question 15Physics

Two capacitors of capacitance 2 μF and 3 μF are connected in series across a 10 V battery. What is the charge on each capacitor?

  1. 20 μC
  2. 30 μC
  3. 5 μC
  4. 12 μC Correct answer.

Explanation

The series equivalent capacitance is C = (2 × 3)/(2 + 3) = 1.2 μF. The charge supplied by the battery is Q = CV = 1.2 μF × 10 V = 12 μC, and capacitors in series carry the same charge.

Question 16Physics

A cell of emf 10 V and internal resistance 2 Ω is connected to an external resistance of 8 Ω. What is the terminal potential difference of the cell?

  1. 8 V Correct answer.
  2. 12.5 V
  3. 2 V
  4. 10 V

Explanation

The current is I = ε/(R + r) = 10/(8 + 2) = 1 A. The terminal potential difference is V = IR = 1 × 8 = 8 V, equivalently ε − Ir = 10 − 2 = 8 V.

Question 17Physics

A proton enters a uniform magnetic field perpendicular to its velocity and moves in a circular path. The radius of this path is directly proportional to which quantity?

  1. 1/v
  2. v Correct answer.
  3. v²
  4. √v

Explanation

The magnetic force provides the centripetal force: qvB = mv²/r. Solving gives r = mv/(qB), so for a given proton and field the radius is directly proportional to the speed v.

Question 18Physics

A ray of light travels from air into a medium of refractive index 1.5. If the angle of incidence is 30°, the angle of refraction is closest to which value?

  1. 45°
  2. 30°
  3. 60°
  4. 19.5° Correct answer.

Explanation

Snell's law gives n₁ sin i = n₂ sin r, so sin r = sin 30° / 1.5 = 0.5 / 1.5 = 0.333. The corresponding angle is r ≈ 19.5°, which is less than the angle of incidence as expected for entry into a denser medium.

Question 19Physics

A uniform rod of mass M and length L is pivoted at one end and held horizontally. It is released from rest. What is the magnitude of its angular acceleration at the instant of release?

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

Explanation

The torque about the pivot is τ = Mg(L/2), and the moment of inertia of a uniform rod about one end is I = ML²/3. Therefore α = τ/I = (MgL/2)/(ML²/3) = 3g/(2L).

Question 20Physics

A sound source of frequency 500 Hz moves directly toward a stationary observer at 20 m/s. Taking the speed of sound as 340 m/s, what frequency does the observer hear?

  1. 500 Hz
  2. 469 Hz
  3. 531 Hz Correct answer.
  4. 540 Hz

Explanation

For a source approaching a stationary observer, the observed frequency is f′ = f v/(v − v_s). Substituting gives f′ = 500 × 340/(340 − 20) = 500 × 340/320 ≈ 531 Hz, which is higher than the emitted frequency.

Question 21Physics

A particle moves in a circle of radius 2 m at a constant speed of 4 m/s. What is the magnitude of its centripetal acceleration?

  1. 16 m/s²
  2. 4 m/s²
  3. 2 m/s²
  4. 8 m/s² Correct answer.

Explanation

Centripetal acceleration has magnitude a = v²/r, so a = 4²/2 = 8 m/s². The speed is constant, so there is no tangential acceleration, but the direction of velocity changes continuously.

Question 22Physics

In a series LCR circuit connected to an alternating source, resonance occurs when which condition is satisfied?

  1. The impedance is equal to zero.
  2. The inductive reactance equals the capacitive reactance. Correct answer.
  3. The resistance equals the inductive reactance.
  4. The inductive reactance is twice the capacitive reactance.

Explanation

Series resonance occurs when X_L = X_C, so the reactances cancel in the impedance expression. The impedance then becomes minimum and equal to R, and the current reaches its maximum value.

Question 23Physics

A convex lens of focal length f forms a real image whose size is equal to the object size. Where must the object be placed?

  1. Between the lens and the focal point
  2. At infinity
  3. At the focal point
  4. At a distance 2f from the lens Correct answer.

Explanation

For a convex lens, an object at 2f produces a real image at 2f on the other side with magnification −1. Thus the image is real, inverted, and equal in size to the object.

Question 24Physics

A stone is thrown horizontally from the top of a tower 20 m high with a speed of 10 m/s. Taking g = 10 m/s² and neglecting air resistance, what is the horizontal distance from the foot of the tower where it lands?

  1. 5 m
  2. 20 m Correct answer.
  3. 40 m
  4. 10 m

Explanation

The vertical motion determines the time of fall: 20 = ½ × 10 × t², giving t = 2 s. The horizontal velocity remains 10 m/s, so the horizontal distance is 10 × 2 = 20 m.

Question 25Physics

A block of mass 5 kg is pulled across a horizontal floor by a rope making 30° with the horizontal with tension 30 N. Taking g = 10 m/s², what is the normal force exerted by the floor on the block?

  1. 15 N
  2. 65 N
  3. 50 N
  4. 35 N Correct answer.

Explanation

The vertical component of tension is T sin 30° = 30 × 0.5 = 15 N upward. Vertical equilibrium gives N + 15 = mg = 50 N, so N = 35 N. The horizontal component of tension does not affect the vertical force balance.

Question 26Physics

A Carnot engine works between a hot reservoir at 500 K and a cold reservoir at 300 K. What is its efficiency?

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

Explanation

For a Carnot engine, efficiency is η = 1 − T_c/T_h, with temperatures in kelvin. Thus η = 1 − 300/500 = 1 − 0.6 = 0.4, or 40%.

Question 27Physics

Two point charges +q and −q are separated by a distance 2a. What is the electric potential at the midpoint of the line joining them?

  1. 2kq/a
  2. Zero Correct answer.
  3. kq/(2a)
  4. kq/a

Explanation

The midpoint is a distance a from each charge. The potential there is kq/a from the positive charge and −kq/a from the negative charge, so the sum is zero. Electric potential is a scalar, so the contributions add algebraically.

Question 28Physics

A uniform metallic wire has resistance R. It is stretched uniformly until its length is doubled. What is its new resistance?

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

Explanation

Stretching at constant volume doubles the length and halves the cross-sectional area. Since R = ρL/A, doubling L and halving A multiplies the resistance by 4.

Question 29Physics

An electron is accelerated from rest through a potential difference of 100 V. Taking h = 6.6×10⁻³⁴ J·s, m_e = 9.1×10⁻³¹ kg and e = 1.6×10⁻¹⁹ C, the de Broglie wavelength is closest to which value?

  1. 1.2×10⁻⁹ m
  2. 1.2×10⁻¹⁰ m Correct answer.
  3. 2.4×10⁻¹⁰ m
  4. 3.7×10⁻¹⁰ m

Explanation

The kinetic energy gained is eV = 1.6×10⁻¹⁷ J. The momentum is p = √(2m_eK) ≈ 5.4×10⁻²⁴ kg·m/s, so λ = h/p ≈ 1.2×10⁻¹⁰ m. This is about 0.12 nm, a typical electron de Broglie wavelength.

Question 30Physics

A uniform solid cylinder rolls without slipping down an incline making an angle θ with the horizontal. What is its linear acceleration along the incline?

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

Explanation

For rolling without slipping, a = g sin θ/(1 + I/MR²). A solid cylinder has I = ½MR², so the denominator is 1 + ½ = 3/2 and a = (2/3)g sin θ. Static friction causes the rotation but does not do net work in pure rolling.

Question 31Physics

The SI unit of impulse is the newton-second (N·s). This unit is dimensionally identical to the unit of which physical quantity?

  1. Angular velocity
  2. Work
  3. Linear momentum Correct answer.
  4. Torque

Explanation

Impulse is force multiplied by time, so its unit N·s reduces to kg·m·s⁻¹. Linear momentum, the product of mass and velocity, has exactly the same unit, which is the content of the impulse–momentum theorem. Torque and work both involve N·m (kg·m²·s⁻²), and angular velocity has the unit s⁻¹.

Question 32Physics

A fixed mass of an ideal gas is heated slowly in a rigid, closed metal container so that its volume cannot change. The work done by the gas in this process is

  1. Equal to the heat absorbed by the gas
  2. Zero Correct answer.
  3. Equal to nRT ln(V₂/V₁)
  4. Equal to the change in internal energy

Explanation

Work done by a gas is given by W = PΔV, and in a rigid container the volume change ΔV is zero, so no pressure–volume work is done. The first law then gives Q = ΔU, meaning the whole of the supplied heat raises the internal energy, but that heat is not the work.

Question 33Physics

A concave mirror of small aperture is held close to the face and used as a shaving mirror. The image of the face seen by the user is

  1. real and erect
  2. real and inverted
  3. virtual and inverted
  4. virtual and erect Correct answer.

Explanation

The face lies between the pole and the principal focus of the concave mirror, so the reflected rays diverge and cannot actually meet. They appear to come from a point behind the mirror, giving a virtual, erect and magnified image, which is why the mirror is suited to shaving.

Question 34Physics

A particle executes simple harmonic motion of amplitude A. At the instant its displacement from the mean position is A/2, the ratio of its kinetic energy to its potential energy is

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

Explanation

For SHM, potential energy is proportional to x² and kinetic energy to (A² − x²). Substituting x = A/2 gives PE ∝ A²/4 and KE ∝ A² − A²/4 = 3A²/4, so the ratio KE : PE is 3 : 1.

Question 35Physics

A point charge q is placed at the centre of a cube of side a, with no other charges nearby. The electric flux through one face of the cube is

  1. q/ε₀
  2. zero
  3. q/6ε₀ Correct answer.
  4. q/8ε₀

Explanation

By Gauss's law the total flux through the closed cube surface is q/ε₀. Because the charge sits at the centre, the six identical faces share this flux equally, so each face carries one-sixth of the total, namely q/6ε₀; the side length a does not appear in the result.

Question 36Physics

A galvanometer of resistance G is converted into an ammeter by connecting a shunt of resistance G/4 across it. What fraction of the total current flows through the galvanometer coil?

  1. 1/4
  2. 1/2
  3. 1/5 Correct answer.
  4. 4/5

Explanation

In a parallel combination the current divides in inverse proportion to resistance, so I_g/I = S/(S + G) with S = G/4. Substituting gives (G/4)/[(G/4) + G] = (G/4)/(5G/4) = 1/5, so one-fifth of the line current passes through the coil and four-fifths through the shunt.

Question 37Physics

A straight wire of length 0.5 m carrying a current of 2 A is placed in a uniform magnetic field of 0.4 T, the wire making an angle of 30° with the field direction. The magnitude of the magnetic force on the wire is

  1. 0.40 N
  2. 0.10 N
  3. 0.35 N
  4. 0.20 N Correct answer.

Explanation

The force on a current-carrying wire in a uniform field is F = BIL sinθ, where θ is the angle between the wire and the field. Here F = 0.4 × 2 × 0.5 × sin 30° = 0.4 × 0.5 = 0.20 N, directed perpendicular to the plane containing the wire and the field.

Question 38Physics

Light of wavelength 400 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. 3.1 eV
  2. 2.0 eV
  3. 1.1 eV Correct answer.
  4. 0.9 eV

Explanation

The photon energy is E = hc/λ = 1240/400 = 3.1 eV. Einstein's photoelectric equation gives the maximum kinetic energy as E − φ = 3.1 − 2.0 = 1.1 eV, the surplus energy appearing as the electron's kinetic energy.

Question 39Physics

A disc of moment of inertia I about its vertical axis spins with angular velocity ω. A second disc of moment of inertia I/2, initially at rest and coaxial with the first, is lowered onto it and the two rotate together without external torque. The fraction of the initial kinetic energy lost is

  1. 1/3 Correct answer.
  2. 5/9
  3. 1/9
  4. 2/3

Explanation

Angular momentum is conserved: Iω = (I + I/2)ω′, so ω′ = 2ω/3. The initial energy is ½Iω² and the final energy is ½(3I/2)(2ω/3)² = (2/3)(½Iω²), so exactly one-third of the original kinetic energy is dissipated as heat and sound during the coupling.

Question 40Physics

A physical quantity is given by P = a²b/√c. In an experiment the percentage errors in the measured values of a, b and c are 1%, 2% and 4% respectively. The maximum percentage error in P is

  1. 7%
  2. 6% Correct answer.
  3. 4%
  4. 8%

Explanation

For a product or quotient, percentage errors add after being multiplied by the magnitude of the corresponding exponent. Hence ΔP/P = 2(1%) + 1(2%) + ½(4%) = 2% + 2% + 2% = 6%, where the exponent of c contributes only half its error because of the square root.

Question 41Physics

A car starts from rest and accelerates uniformly at 2 m/s² along a straight road for 5 s. What distance does it cover in this interval?

  1. 10 m
  2. 50 m
  3. 20 m
  4. 25 m Correct answer.

Explanation

For uniform acceleration from rest, the displacement is s = ½at². Here a = 2 m/s² and t = 5 s, so s = ½ × 2 × 25 = 25 m. The final speed is 10 m/s, but the car does not travel at that speed throughout.

Question 42Physics

Which of the following is the SI unit of magnetic flux?

  1. henry (H)
  2. farad (F)
  3. tesla (T)
  4. weber (Wb) Correct answer.

Explanation

Magnetic flux is defined as Φ = B·A, so its unit is the product of tesla and square metre, which is the weber. The tesla measures magnetic flux density, the henry measures inductance, and the farad measures capacitance.

Question 43Physics

An ideal gas absorbs 200 J of heat while doing 80 J of work on its surroundings. What is the change in its internal energy?

  1. 80 J
  2. 280 J
  3. 200 J
  4. 120 J Correct answer.

Explanation

The first law of thermodynamics gives ΔU = Q − W, with Q positive for heat absorbed and W positive for work done by the gas. Substituting Q = 200 J and W = 80 J gives ΔU = 120 J. Internal energy rises because the heat input exceeds the work output.

Question 44Physics

A parallel-plate capacitor is charged by a battery and then disconnected. The separation between the plates is doubled while the charge remains constant. The potential difference between the plates:

  1. becomes double Correct answer.
  2. remains unchanged
  3. becomes half
  4. becomes four times

Explanation

With the battery disconnected, the charge Q on the plates stays fixed. Capacitance is C = ε₀A/d, so doubling d halves C; since V = Q/C, the potential difference doubles. The electric field between the plates remains unchanged in this process.

Question 45Physics

In a Wheatstone bridge, the arms are P = 10 Ω and Q = 20 Ω in one branch, and R = 15 Ω and S in the other, with the galvanometer connected between the junctions of P–R and Q–S. What value of S balances the bridge?

  1. 20 Ω
  2. 30 Ω Correct answer.
  3. 7.5 Ω
  4. 45 Ω

Explanation

A Wheatstone bridge is balanced when the resistance ratios in the two branches are equal: P/Q = R/S. Substituting gives 10/20 = 15/S, so S = 30 Ω. At balance no current flows through the galvanometer.

Question 46Physics

The critical angle for total internal reflection at a glass–air interface, taking the refractive index of glass as 1.5, is closest to:

  1. 41.8° Correct answer.
  2. 60.0°
  3. 30.0°
  4. 48.6°

Explanation

At the critical angle the refracted ray grazes the surface, so Snell's law reduces to sin C = 1/n. With n = 1.5, sin C = 2/3 and C ≈ 41.8°. For incidence angles larger than this, total internal reflection occurs.

Question 47Physics

An electron and a proton have the same kinetic energy. The ratio of the de Broglie wavelength of the electron to that of the proton is closest to:

  1. 1836
  2. 43 Correct answer.
  3. 1
  4. 1/43

Explanation

The de Broglie wavelength is λ = h/√(2mK). For equal kinetic energy, λ is inversely proportional to √m, so the lighter electron has the longer wavelength. The ratio is λ_e/λ_p = √(m_p/m_e) ≈ √1836 ≈ 43.

Question 48Physics

A uniform rod of mass M and length L is hinged at one end and held horizontally. It is released from rest and swings in a vertical plane. What is its angular speed when it becomes vertical?

  1. √(2g/L)
  2. √(6g/L)
  3. √(3g/L) Correct answer.
  4. √(g/L)

Explanation

Energy conservation gives Mg(L/2) = ½Iω², and for a rod hinged at one end I = ML²/3. Solving, ω² = 3g/L, so ω = √(3g/L). The centre of mass falls a vertical distance L/2.

Question 49Physics

A conducting rod of length 0.5 m rotates about one end in a plane perpendicular to a uniform magnetic field of 0.2 T at 10 rad/s. The emf induced between its ends is:

  1. 1.00 V
  2. 0.05 V
  3. 0.25 V Correct answer.
  4. 0.50 V

Explanation

For a rod rotating about one end in a perpendicular field, the motional emf is ½BωL². Substituting B = 0.2 T, ω = 10 rad/s and L = 0.5 m gives ½ × 0.2 × 10 × 0.25 = 0.25 V.

Question 50Physics

A source emitting sound of frequency 500 Hz moves directly toward a stationary observer at 34 m/s. Taking the speed of sound in air as 340 m/s, the frequency heard by the observer is:

  1. 555.6 Hz Correct answer.
  2. 500 Hz
  3. 450 Hz
  4. 606 Hz

Explanation

When the source approaches a stationary observer, the observed frequency is f' = f v/(v − v_s). Here f' = 500 × 340/(340 − 34) ≈ 555.6 Hz, higher than the emitted frequency because the wavefronts are compressed.