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Question 1Physics

A body 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?

  1. 1.25 m/s²
  2. 5 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 = (15 − 5)/4 = 2.5 m/s². The change in velocity is 10 m/s and dividing by the 4 s interval gives the result.

Question 2Physics

A projectile is launched at an angle with the horizontal in the absence of air resistance. Which quantity stays constant throughout the flight?

  1. Vertical component of velocity
  2. Horizontal component of velocity
  3. Magnitude of acceleration Correct answer.
  4. Speed of the projectile

Explanation

The only force acting is gravity, which is constant in magnitude and direction, so the acceleration (g, downward) is constant. The horizontal velocity component is also constant, but the question asks about acceleration; the vertical component and the speed change continuously.

Question 3Physics

Two masses, 3 kg and 5 kg, are connected by a light string over a frictionless pulley (Atwood machine). Taking g = 10 m/s², what is the acceleration of the system?

  1. 1.25 m/s²
  2. 2.5 m/s² Correct answer.
  3. 10 m/s²
  4. 5 m/s²

Explanation

The net driving force is (m₂ − m₁)g = (5 − 3)(10) = 20 N and the total mass moved is 8 kg. Thus a = 20/8 = 2.5 m/s².

Question 4Physics

A block of mass 2 kg is pushed across a rough horizontal floor by a horizontal force of 12 N. If the coefficient of kinetic friction is 0.2 and g = 10 m/s², what is the acceleration of the block?

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

Explanation

Friction force is μmg = 0.2 × 2 × 10 = 4 N, so the net force is 12 − 4 = 8 N. Dividing by the mass gives a = 8/2 = 4 m/s².

Question 5Physics

A satellite orbits Earth in a circular orbit of radius r. If the orbital radius is increased to 4r while keeping the same central mass, the orbital speed becomes

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

Explanation

For a circular orbit, gravitational force provides the centripetal force: GMm/r² = mv²/r, so v = √(GM/r). Increasing r by a factor of 4 reduces v by √4 = 2, giving half the original speed.

Question 6Physics

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 common velocity after the collision?

  1. 1.5 m/s
  2. 1 m/s Correct answer.
  3. 0.5 m/s
  4. 3 m/s

Explanation

In a perfectly inelastic collision, momentum is conserved: m₁u₁ = (m₁ + m₂)v. Thus v = (2 × 3)/(2 + 4) = 6/6 = 1 m/s.

Question 7Physics

A force of 10 N acts on a body and displaces it by 2 m. If the force acts at 60° to the displacement, the work done is

  1. 17.3 J
  2. 20 J
  3. 0 J
  4. 10 J Correct answer.

Explanation

Work is W = Fd cos θ = 10 × 2 × cos 60° = 20 × 0.5 = 10 J. Only the component of force along the displacement does work.

Question 8Physics

A spring of spring constant 200 N/m is compressed by 0.1 m. The elastic potential energy stored is

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

Explanation

Elastic potential energy is U = ½kx² = ½ × 200 × (0.1)² = 100 × 0.01 = 1 J. The displacement is squared, so the small compression stores little energy.

Question 9Physics

A solid cylinder rolls without slipping. Its moment of inertia about its central axis is I=MR²/2. What fraction of its total kinetic energy is rotational?

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

Explanation

With ω=v/R, rotational energy is Iω²/2=Mv²/4. Translational energy is Mv²/2, so total energy is 3Mv²/4 and the rotational fraction is one third.

Question 10Physics

The moment of inertia of a uniform rod of mass M and length L about an axis through its centre and perpendicular to its length is

  1. ML²
  2. ML²/12 Correct answer.
  3. ML²/2
  4. ML²/3

Explanation

For a uniform rod about a perpendicular axis through its centre, I = ML²/12. The ML²/3 value applies to an axis through one end, by the parallel-axis theorem.

Question 11Physics

The escape velocity from the surface of a planet of mass M and radius R is given by

  1. √(GM/R)
  2. √(GM/2R)
  3. 2GM/R
  4. √(2GM/R) Correct answer.

Explanation

Setting kinetic energy equal to the magnitude of gravitational potential energy gives ½mv² = GMm/R, so v = √(2GM/R). The factor 2 arises because the potential energy at the surface is −GMm/R.

Question 12Physics

A simple pendulum has a period T on Earth. On a planet where the acceleration due to gravity is four times that on Earth, the period of the same pendulum becomes

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

Explanation

The period of a simple pendulum is T = 2π√(L/g), so T ∝ 1/√g. Quadrupling g reduces the period by √4 = 2, giving T/2.

Question 13Physics

A particle executes simple harmonic motion with amplitude A. At the point where its displacement is half the amplitude, what fraction of its total energy is kinetic?

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

Explanation

Total energy E = ½kA² and potential energy U = ½kx². At x = A/2, U = ½k(A/2)² = E/4, so kinetic energy is E − E/4 = 3E/4.

Question 14Physics

The speed of sound in air is approximately 340 m/s. A source emits a sound of frequency 170 Hz. What is the wavelength?

  1. 1 m
  2. 2 m Correct answer.
  3. 0.5 m
  4. 57800 m

Explanation

For a wave, v = fλ, so λ = v/f = 340/170 = 2 m. Frequency and wavelength are inversely related for a fixed wave speed.

Question 15Physics

In a stationary wave on a stretched string fixed at both ends, the distance between two consecutive nodes is

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

Explanation

Adjacent nodes in a stationary wave are separated by half a wavelength, λ/2. The same separation holds between consecutive antinodes.

Question 16Physics

Two point charges are separated by a distance d in vacuum. If the distance is doubled while the charges are unchanged, the electrostatic force between them 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 F = kq₁q₂/d², so force is inversely proportional to the square of separation. Doubling d divides the force by 4.

Question 17Physics

Three capacitors of 3 μF each are connected in series. The equivalent capacitance of the combination is

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

Explanation

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

Question 18Physics

A wire of resistance R is stretched uniformly so that its length is doubled while its volume stays constant. The new resistance is

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

Explanation

Stretching to double length halves the cross-sectional area (volume constant), and R = ρL/A. Both L doubling and A halving multiply resistance by 4, giving 4R.

Question 19Physics

Two resistors of 6 Ω and 3 Ω are connected in parallel across a 6 V battery of negligible internal resistance. The total current drawn from the battery is

  1. 2 A
  2. 0.67 A
  3. 1 A
  4. 3 A Correct answer.

Explanation

The parallel equivalent is (6 × 3)/(6 + 3) = 2 Ω. Total current is I = V/R = 6/2 = 3 A, which also equals 1 A + 2 A through the branches.

Question 20Physics

A charged particle moves parallel to a uniform magnetic field. The magnetic force on the particle is

  1. zero Correct answer.
  2. maximum
  3. along the velocity
  4. perpendicular to the field

Explanation

The magnetic force is F = qvB sin θ, where θ is the angle between velocity and field. When the particle moves parallel to the field, θ = 0 and sin θ = 0, so the force is zero.

Question 21Physics

A step-down transformer has 1000 turns in the primary and 200 turns in the secondary. If the primary is connected to a 220 V AC supply, the secondary voltage is

  1. 22 V
  2. 44 V Correct answer.
  3. 220 V
  4. 1100 V

Explanation

For an ideal transformer, V₂/V₁ = N₂/N₁, so V₂ = 220 × (200/1000) = 44 V. A step-down transformer reduces voltage in proportion to the turns ratio.

Question 22Physics

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. 4.48 eV
  3. 0.24 eV
  4. 0.48 eV Correct answer.

Explanation

Photon energy is E = hc/λ = 1240/500 = 2.48 eV. By Einstein's photoelectric equation, Kmax = E − φ = 2.48 − 2.0 = 0.48 eV.

Question 23Physics

In the Bohr model of the hydrogen atom, the radius of the nth orbit is proportional to

  1. 1/n²
  2. 1/n
  3. n² Correct answer.
  4. n

Explanation

The Bohr radius is rₙ = n²h²ε₀/(πme²), so orbital radius scales as n². The ground state has n = 1, and higher orbits are progressively farther out.

Question 24Physics

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

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

Explanation

Thirty days correspond to three half-lives (30/10 = 3). After each half-life the remaining fraction halves, so the fraction left is (1/2)³ = 1/8.

Question 25Physics

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

  1. 30 cm Correct answer.
  2. 15 cm
  3. 6 cm
  4. 10 cm

Explanation

Using the lens formula 1/f = 1/v − 1/u with u = −15 cm and f = +10 cm gives 1/v = 1/10 + 1/(−15) = 1/30, so v = 30 cm. The positive sign confirms a real image on the far side.

Question 26Physics

A car travels 100 m due east and then 100 m due north. What is the magnitude of its resultant displacement?

  1. 200 m
  2. 141 m Correct answer.
  3. 100 m
  4. 0 m

Explanation

The two displacements are perpendicular, so the resultant is found from the Pythagorean relation: sqrt(100² + 100²) = 100√2 ≈ 141 m. Displacement depends only on the initial and final positions, not on the path taken.

Question 27Physics

A ball is thrown vertically upward with a speed of 20 m/s. Taking g = 10 m/s², how long does it take to reach its highest point?

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

Explanation

At the highest point the vertical velocity is momentarily zero, so using v = u − gt gives 0 = 20 − 10t, hence t = 2 s. The acceleration due to gravity acts opposite to the upward motion throughout the rise.

Question 28Physics

A block of mass 5 kg rests on a horizontal surface 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. 20 N Correct answer.
  2. 2 N
  3. 0.4 N
  4. 50 N

Explanation

The limiting static friction equals μs times the normal force, and on a horizontal surface the normal force equals the weight mg = 50 N. Thus f = 0.4 × 50 = 20 N, which is the minimum applied force needed to overcome it.

Question 29Physics

The dimensional formula of the universal gravitational constant G is

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

Explanation

From F = Gm₁m₂/r², G = Fr²/(m₁m₂), so its dimensions are those of force times length squared divided by mass squared. Substituting [M L T⁻²][L²]/[M²] gives [M⁻¹ L³ T⁻²].

Question 30Physics

Two satellites orbit a planet at radii R and 4R from its centre. What is the ratio of their orbital periods T₁ : T₂?

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

Explanation

Kepler's third law states that T² is proportional to r³, so T ∝ r^(3/2). With r₂/r₁ = 4, the period ratio is 4^(3/2) = 8, giving T₁ : T₂ = 1 : 8.

Question 31Physics

A body of mass 2 kg moving at 6 m/s collides with a stationary 4 kg body. After the collision the 2 kg body moves at 2 m/s in the same direction. What is the speed of the 4 kg body?

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

Explanation

Momentum is conserved in the collision: (2)(6) + 0 = (2)(2) + (4)v. This gives 12 = 4 + 4v, so v = 2 m/s. The answer is independent of whether the collision is elastic.

Question 32Physics

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. 0.25 rad/s²
  2. 4 rad/s² Correct answer.
  3. 100 rad/s²
  4. 2 rad/s²

Explanation

With uniform angular acceleration, ω = ω₀ + αt. Since ω₀ = 0, α = ω/t = 20/5 = 4 rad/s². The units are radians per second squared.

Question 33Physics

A solid cylinder of mass M and radius R rotates about its central axis. Its moment of inertia is

  1. ⅓MR²
  2. ½MR² Correct answer.
  3. MR²
  4. ⅖MR²

Explanation

For a uniform solid cylinder about its own central axis, the moment of inertia is ½MR², obtained by integrating r²dm over the circular cross-section. This is smaller than MR² because most of the mass lies closer to the axis than R.

Question 34Physics

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

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

Explanation

For an incompressible fluid in steady flow, the equation of continuity gives A₁v₁ = A₂v₂. Thus v₂ = (A)/(A/3) × v = 3v, so the fluid moves three times faster in the narrow section.

Question 35Physics

A body floats in equilibrium with 60% of its volume submerged in water. What is its density?

  1. 1600 kg/m³
  2. 1000 kg/m³
  3. 600 kg/m³ Correct answer.
  4. 400 kg/m³

Explanation

For a floating body, the weight equals the buoyant force, so the body's density divided by the fluid density equals the submerged fraction. Hence the density is 0.6 × 1000 = 600 kg/m³.

Question 36Physics

An ideal gas undergoes an isothermal expansion at temperature T. The work done by the gas is

  1. nR(T₂ − T₁)
  2. nCv(T₂ − T₁)
  3. nRT ln(V₂/V₁) Correct answer.
  4. zero

Explanation

In an isothermal process the internal energy stays constant, so the heat absorbed equals the work done. Integrating P dV with P = nRT/V gives W = nRT ln(V₂/V₁).

Question 37Physics

A Carnot engine operates between reservoirs at 500 K and 300 K. Its efficiency is

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

Explanation

The efficiency of a Carnot engine is 1 − T_cold/T_hot, using absolute temperatures. Here 1 − 300/500 = 0.4, that is, 40%.

Question 38Physics

In a stationary wave on a stretched string fixed at both ends, the distance between two consecutive antinodes is

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

Explanation

Adjacent antinodes are separated by half a wavelength, just as adjacent nodes are. Between two successive antinodes the string completes one full excursion from maximum positive to maximum negative displacement.

Question 39Physics

A sound source moves toward a stationary observer with speed v/5, where v is the speed of sound. If the source frequency is f, the observed frequency is

  1. 1.5f
  2. 0.8f
  3. 1.25f Correct answer.
  4. 1.2f

Explanation

For a source approaching a stationary observer, the observed frequency is f′ = f × v/(v − v_s). With v_s = v/5 this gives f′ = f × v/(4v/5) = 1.25f.

Question 40Physics

A charge of 2 μC is placed at a point where the electric potential is 500 V. The electric potential energy of the charge is

  1. 4 × 10⁻⁹ J
  2. 2.5 × 10⁻⁴ J
  3. 1 × 10⁻⁶ J
  4. 1 × 10⁻³ J Correct answer.

Explanation

The potential energy of a charge q at potential V is U = qV. Thus U = (2 × 10⁻⁶)(500) = 1 × 10⁻³ J.

Question 41Physics

A 12 V battery of negligible internal resistance is connected across two resistors of 4 Ω and 8 Ω in series. The current in the circuit is

  1. 1.5 A
  2. 0.5 A
  3. 3 A
  4. 1 A Correct answer.

Explanation

In series the resistances add, giving a total of 12 Ω. Ohm's law then gives I = V/R = 12/12 = 1 A, and the same current flows through both resistors.

Question 42Physics

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

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

Explanation

A low shunt in parallel diverts most of the current: (I − Ig)S = IgG. Here (1 − 0.001)S = (0.001)(50), so S ≈ 0.05 Ω.

Question 43Physics

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

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

Explanation

The magnetic force qv × B is always perpendicular to the velocity, so it changes only the direction and not the speed. A constant force of fixed magnitude acting perpendicular to the motion produces uniform circular motion.

Question 44Physics

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

  1. The impedance is maximum and equals R
  2. The power factor is zero
  3. The current is zero
  4. The impedance is minimum and equals R Correct answer.

Explanation

At resonance the inductive and capacitive reactances are equal and cancel, so the impedance is purely resistive and equal to R, its minimum possible value. The current is then maximum and the power factor is unity.

Question 45Physics

An electromagnetic wave travels in vacuum in the positive x-direction. At a point where the electric field points along +y, the magnetic field points along

  1. −y
  2. +x
  3. −z
  4. +z Correct answer.

Explanation

In an electromagnetic wave, E × B gives the direction of propagation. Since E is along +y and propagation is along +x, B must point along +z so that ŷ × ẑ = x̂.

Question 46Physics

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

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

Explanation

Fringe width is β = λD/d, so it is directly proportional to the screen distance and inversely proportional to the slit separation. Halving D and doubling d gives β′ = β × (1/2)/(2) = β/4.

Question 47Physics

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

  1. √V
  2. V²
  3. 1/√V Correct answer.
  4. V

Explanation

The kinetic energy gained is eV, so the momentum is p = √(2meV) and the de Broglie wavelength λ = h/p is proportional to 1/√V. Increasing the accelerating voltage shortens the wavelength.

Question 48Physics

A radioactive nucleus undergoes alpha decay. The mass number and atomic number of the daughter nucleus change respectively by

  1. −1 and −1
  2. −4 and −4
  3. −2 and −4
  4. −4 and −2 Correct answer.

Explanation

An alpha particle is a helium nucleus with mass number 4 and atomic number 2. Emitting it reduces the parent's mass number by 4 and its atomic number by 2.

Question 49Physics

A ray of light passes from glass of refractive index 1.5 into water of refractive index 1.33. As it enters the water, the ray

  1. travels undeviated
  2. bends toward the normal
  3. undergoes total internal reflection
  4. bends away from the normal Correct answer.

Explanation

Light bends away from the normal when it moves into a medium of lower refractive index, because the speed of light increases. Here 1.33 < 1.5, so the angle of refraction is greater than the angle of incidence.

Question 50Physics

A converging lens of focal length 20 cm is used to form an image of an object placed at 30 cm from it. The image is

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

Explanation

Using 1/v − 1/u = 1/f with u = −30 cm and f = +20 cm gives v = +60 cm, so the image is real. The magnification m = v/u = −2 means it is inverted and twice as large.