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Question 1Physics

A car starts from rest and accelerates uniformly at 2 m/s² along a straight road for 5 s. How far does it travel during this interval?

  1. 10 m
  2. 50 m
  3. 25 m Correct answer.
  4. 100 m

Explanation

For uniform acceleration from rest, the displacement is s = ½at². Substituting a = 2 m/s² and t = 5 s gives s = ½ × 2 × 25 = 25 m. Equivalently, the final speed is 10 m/s and the average speed is 5 m/s.

Question 2Physics

Two forces of 3 N and 4 N act at right angles on a particle. What is the magnitude of the resultant force?

  1. 7 N
  2. 1 N
  3. 5 N Correct answer.
  4. 12 N

Explanation

For two perpendicular vectors, the resultant magnitude is found with the Pythagorean theorem: R = √(3² + 4²) = 5 N. The direction is inclined at tan⁻¹(4/3) to the 3 N force.

Question 3Physics

A force of 10 N acts on a block and moves it 3 m along a straight line. If the force makes an angle of 60° with the displacement, what is the work done by the force?

  1. 15 J Correct answer.
  2. 0 J
  3. 30 J
  4. 26 J

Explanation

Work is the dot product W = Fd cosθ. With F = 10 N, d = 3 m and θ = 60°, W = 10 × 3 × 0.5 = 15 J. The cosine factor accounts for only the component of force along the displacement.

Question 4Physics

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

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

Explanation

Centripetal acceleration has magnitude a_c = v²/r even when the speed is constant. Substituting v = 4 m/s and r = 2 m gives a_c = 16/2 = 8 m/s², directed toward the centre of the circle.

Question 5Physics

At a height equal to the Earth's radius above the Earth's surface, what is the acceleration due to gravity compared with its value at the surface?

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

Explanation

Gravity follows the inverse-square law, g = GM/r², where r is measured from Earth's centre. At height R above the surface, r = 2R, so g' = GM/(2R)² = g/4.

Question 6Physics

A simple pendulum has a period of 2 s. If its length is increased to four times the original length, what is the new period?

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

Explanation

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

Question 7Physics

A gas absorbs 200 J of heat and does 80 J of work on its surroundings. What is the change in the internal energy of the gas?

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

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. Thus ΔU = 200 J − 80 J = 120 J.

Question 8Physics

Two point charges attract each other with force F. If one charge is doubled and the distance between them is halved, what is the magnitude of the new force?

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

Explanation

Coulomb's law gives F = kq₁q₂/r². Doubling one charge doubles the force, and halving the distance multiplies it by 1/(1/2)² = 4, so the net factor is 2 × 4 = 8.

Question 9Physics

A proton and an alpha particle are accelerated from rest through the same potential difference and then enter a uniform magnetic field perpendicular to their velocities. What is the ratio of the radius of the proton's path to that of the alpha particle?

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

Explanation

For a charge accelerated through potential V, r = mv/(qB) with v = √(2qV/m), so r = √(2mV/q)/B and r ∝ √(m/q). For a proton m/q = m/e, while for an alpha particle m/q = 4m/(2e) = 2m/e; hence r_p/r_α = √(1/2) = 1/√2.

Question 10Physics

A metal surface has threshold wavelength λ₀. Light of wavelength λ₀/2 is incident on it. What is the maximum kinetic energy of the emitted photoelectrons?

  1. hc/λ₀ Correct answer.
  2. 3hc/λ₀
  3. hc/(2λ₀)
  4. 2hc/λ₀

Explanation

The photon energy at wavelength λ₀/2 is E = hc/(λ₀/2) = 2hc/λ₀. The work function is Φ = hc/λ₀, so Einstein's photoelectric equation gives Kmax = E − Φ = hc/λ₀.

Question 11Physics

The SI unit of electric flux is

  1. N/C
  2. N·m²/C Correct answer.
  3. J/C
  4. C/m²

Explanation

Electric flux is the dot product of electric field and area, so its unit is (N/C)·m² = N·m²/C. This also equals V·m in SI, but N·m²/C is the standard derived form.

Question 12Physics

A rigid body is in translational equilibrium. Which condition must hold for the forces acting on it?

  1. The vector sum of the forces must be zero. Correct answer.
  2. The forces must act through a single point.
  3. The sum of the force magnitudes must be zero.
  4. All forces must have equal magnitude.

Explanation

Translational equilibrium means the resultant force is zero, so the vector sum of all external forces must vanish. Equal magnitudes or a common line of action are not required; only the vector addition must cancel.

Question 13Physics

For a projectile moving under gravity with negligible air resistance, which quantity remains constant throughout the flight?

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

Explanation

In projectile motion the horizontal acceleration is zero, so the horizontal velocity component stays constant. The vertical component changes because of gravity, and therefore speed and kinetic energy also change.

Question 14Physics

A 2.0 kg block slides down a rough plane inclined at 30° to the horizontal at constant velocity. What is the coefficient of kinetic friction between the block and the plane?

  1. 1.00
  2. 0.58 Correct answer.
  3. 0.87
  4. 0.50

Explanation

At constant velocity the forces along the incline balance: mg sin30° = μ_k mg cos30°. The mass cancels, giving μ_k = tan30° ≈ 0.58.

Question 15Physics

A satellite moves in a circular orbit of radius 2R about Earth, where R is Earth's radius. Taking g as the acceleration due to gravity at Earth's surface, what is the satellite's orbital speed?

  1. √(gR/2) Correct answer.
  2. √(gR/4)
  3. √(2gR)
  4. √(gR)

Explanation

For a circular orbit, v² = GM/r. At r = 2R this becomes v² = GM/(2R), and since GM = gR² at the surface, v = √(gR/2).

Question 16Physics

An ideal gas expands isothermally and does positive work on its surroundings. Which statement is correct for this process?

  1. No heat is exchanged with the surroundings.
  2. The temperature of the gas decreases in proportion to the work done.
  3. The heat absorbed by the gas equals the work done by the gas. Correct answer.
  4. The internal energy of the gas increases by the work done.

Explanation

For an ideal gas, internal energy depends only on temperature. In an isothermal process ΔT = 0, so ΔU = 0 and the first law gives Q = W: heat absorbed equals work done by the gas.

Question 17Physics

Two identical capacitors, each of capacitance C, are connected first in series and then in parallel across the same ideal battery. What is the ratio of the total energy stored in the parallel combination to that in the series combination?

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

Explanation

The series equivalent capacitance is C/2, while the parallel equivalent is 2C. Since stored energy is ½C_eqV² at the same voltage, the parallel-to-series energy ratio is (2C)/(C/2) = 4.

Question 18Physics

A uniform metal wire of resistance R is stretched uniformly until its length is doubled, with volume unchanged. What is the new resistance?

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

Explanation

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

Question 19Physics

A charged particle moving with speed v enters a uniform magnetic field at an angle θ to the field. The particle follows a helical path. If θ is reduced from 90° to 30° while v is unchanged, what happens to the radius and pitch of the helix?

  1. Radius doubles and pitch decreases.
  2. Radius halves and pitch becomes nonzero. Correct answer.
  3. Radius stays unchanged and pitch increases.
  4. Radius halves and pitch decreases.

Explanation

The magnetic force depends on the component of velocity perpendicular to B, v sinθ. Changing θ from 90° to 30° halves sinθ, so the radius r = mv sinθ/(qB) halves. The pitch depends on v cosθ and becomes nonzero because a parallel velocity component now exists.

Question 20Physics

In a Young's double-slit experiment, the slit separation is halved and the distance from the slits to the screen is doubled. The fringe width becomes

  1. one-quarter of the original width
  2. 4 times the original width Correct answer.
  3. 2 times the original width
  4. half the original width

Explanation

Fringe width is β = λD/d. Halving d multiplies β by 2, and doubling D multiplies it by another factor of 2, so the new width is 4β.

Question 21Physics

A particle undergoing simple harmonic motion is at its maximum displacement from equilibrium. Which statement correctly describes its acceleration at that instant?

  1. It is constant and independent of displacement.
  2. It is zero because the velocity is momentarily zero.
  3. It is maximum and directed away from the equilibrium position.
  4. It is maximum and directed toward the equilibrium position. Correct answer.

Explanation

In simple harmonic motion the acceleration is given by a = −ω²x. At maximum displacement the magnitude of x is greatest, so the acceleration has maximum magnitude and points back toward equilibrium. The velocity is zero there, but that does not make the acceleration zero.

Question 22Physics

The SI unit of capacitance is the

  1. ohm (Ω)
  2. volt per metre (V m⁻¹)
  3. coulomb (C)
  4. farad (F) Correct answer.

Explanation

Capacitance is defined by C = Q/V, so its unit is the coulomb per volt, which is named the farad (F). The farad is therefore the SI unit of capacitance, not of charge, field, or resistance.

Question 23Physics

The dimensional formula of impulse is

  1. ML²T⁻²
  2. ML⁻¹T⁻¹
  3. MLT⁻¹ Correct answer.
  4. MLT⁻²

Explanation

Impulse equals force multiplied by the time for which it acts, so its dimensions are those of force times time. Since force has dimensions MLT⁻², impulse has dimensions MLT⁻¹, the same as momentum.

Question 24Physics

A solid cylinder rolls without slipping down an incline. What fraction of its total kinetic energy is rotational kinetic energy?

  1. two-fifths
  2. one-fifth
  3. one-third Correct answer.
  4. one-half

Explanation

For a solid cylinder rolling without slipping, I = ½MR² and v = ωR. The rotational kinetic energy is ¼Mv² while the total kinetic energy is ¾Mv², so the rotational fraction is (¼)/(¾) = ⅓.

Question 25Physics

Water flows steadily through a horizontal pipe whose cross-sectional area decreases by a factor of two. If the speed in the wider section is 2.0 m/s and water density is 1000 kg/m³, what is the pressure drop from the wider to the narrower section? Assume ideal, incompressible flow.

  1. 12000 Pa
  2. 3000 Pa
  3. 1500 Pa
  4. 6000 Pa Correct answer.

Explanation

By continuity, halving the cross-sectional area doubles the speed, so the narrow-section speed is 4.0 m/s. Bernoulli's equation for a horizontal pipe gives Δp = ½ρ(v₂² − v₁²) = ½(1000)(16 − 4) = 6000 Pa.

Question 26Physics

A sound wave of frequency 500 Hz travels in air at 340 m/s. What is the phase difference between two points along the direction of propagation that are 0.17 m apart?

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

Explanation

The wavelength is λ = v/f = 340/500 = 0.68 m. The separation 0.17 m is λ/4, and a path difference of λ/4 corresponds to a phase difference of 2π/4 = π/2 rad.

Question 27Physics

A straight conducting rod of length 0.50 m moves with speed 4.0 m/s perpendicular to a uniform magnetic field of flux density 0.20 T. What motional emf is induced across the rod?

  1. 0.80 V
  2. 0.40 V Correct answer.
  3. 0.10 V
  4. 0.20 V

Explanation

The motional emf for a rod moving perpendicular to a uniform field is ε = Blv. Substituting B = 0.20 T, l = 0.50 m and v = 4.0 m/s gives ε = 0.40 V.

Question 28Physics

An ideal gas is heated at constant volume so that its absolute temperature doubles. By what factor does the root-mean-square speed of its molecules change?

  1. It increases by a factor of √2. Correct answer.
  2. It remains unchanged.
  3. It increases by a factor of 2.
  4. It increases by a factor of 4.

Explanation

The root-mean-square speed is v_rms = √(3RT/M), so it is proportional to √T at constant volume. Doubling the absolute temperature therefore multiplies v_rms by √2.

Question 29Physics

A 2.0 μF capacitor charged to 50 V is disconnected from the supply and then connected in parallel with an uncharged 3.0 μF capacitor. What is the energy dissipated during the charge sharing?

  1. 1.0 mJ
  2. 2.5 mJ
  3. 0.50 mJ
  4. 1.5 mJ Correct answer.

Explanation

The initial charge is Q = CV = (2.0 μF)(50 V) = 100 μC. After connection the common potential is V' = Q/(C₁+C₂) = 100 μC/5.0 μF = 20 V. Initial energy is 2.5 mJ, final energy is 1.0 mJ, so 1.5 mJ is dissipated.

Question 30Physics

An electron and a proton have the same de Broglie wavelength. What is the ratio K_e/K_p of their kinetic energies? Use m_p ≈ 1836 m_e.

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

Explanation

For the same de Broglie wavelength, λ = h/p, the electron and proton have the same momentum magnitude. Since K = p²/2m, the kinetic energy is inversely proportional to mass, so K_e/K_p = m_p/m_e ≈ 1836.

Question 31Physics

The dimensional formula of Planck's constant is

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

Explanation

Planck's constant has units of joule-second. Since the joule is kg m² s⁻², multiplying by seconds gives dimensions M L² T⁻¹, which are also the dimensions of angular momentum.

Question 32Physics

A concave lens forms an image of a real object placed in front of it. The image is always

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

Explanation

A concave lens is diverging, so rays from a real object leave the lens as if they came from a point on the same side. The image is therefore virtual, erect and diminished for every real object position.

Question 33Physics

The SI unit of inductance is the

  1. tesla
  2. henry Correct answer.
  3. farad
  4. weber

Explanation

Inductance is flux linkage per unit current, so its unit is the weber per ampere, which is defined as the henry. The farad measures capacitance, the tesla magnetic flux density and the weber magnetic flux.

Question 34Physics

A 5.0 kg crate is lifted vertically at constant speed through a height of 2.0 m. Taking g = 9.8 m/s², what is the work done by the lifting force?

  1. 196 J
  2. 0 J
  3. 98 J Correct answer.
  4. 49 J

Explanation

Because the crate moves at constant speed, the lifting force equals its weight, mg = 5.0 × 9.8 = 49 N. The work done by this force is Fd = 49 × 2.0 = 98 J; gravity does −98 J, so the net work is zero.

Question 35Physics

A car rounds a flat horizontal curve of radius 50 m at a constant speed of 15 m/s. What is the minimum coefficient of static friction between tyres and road needed to prevent skidding? (g = 9.8 m/s²)

  1. 0.23
  2. 0.46 Correct answer.
  3. 0.92
  4. 1.38

Explanation

The required centripetal force is supplied by static friction, so μmg = mv²/r. Cancelling m gives μ = v²/(rg) = (15)²/(50 × 9.8) ≈ 0.46.

Question 36Physics

Two resistors of 6 Ω and 3 Ω are connected in parallel across a 12 V ideal battery. What total power is dissipated in the two resistors?

  1. 16 W
  2. 48 W
  3. 24 W
  4. 72 W Correct answer.

Explanation

The parallel equivalent resistance is given by 1/R = 1/6 + 1/3 = 1/2, so R = 2 Ω. Total power is V²/R = (12)²/2 = 72 W, equal to 24 W in the 6 Ω resistor plus 48 W in the 3 Ω resistor.

Question 37Physics

A convex lens of focal length 20 cm forms an image of an object placed 30 cm from the lens. What is the image distance from the lens?

  1. 30 cm
  2. 10 cm
  3. 12 cm
  4. 60 cm Correct answer.

Explanation

The thin-lens equation is 1/f = 1/do + 1/di. Substituting f = 20 cm and do = 30 cm gives 1/di = 1/20 − 1/30 = 1/60, so di = 60 cm.

Question 38Physics

An ideal gas is compressed adiabatically and quasi-statically. Which statement about the gas is correct?

  1. Its pressure remains constant while its volume decreases.
  2. Its temperature rises because work is done on the gas. Correct answer.
  3. Its internal energy decreases while work is done by the gas.
  4. Its temperature falls because no heat enters.

Explanation

Adiabatic compression means Q = 0 while work is done on the gas, so its internal energy increases. For an ideal gas, internal energy depends on temperature, so the temperature rises and the pressure increases as the volume decreases.

Question 39Physics

A uniform rod of length L and mass M is pivoted at one end and released from rest in the horizontal position. What is its angular speed when it reaches the vertical position? (Moment of inertia about the pivot = ML²/3.)

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

Explanation

The centre of mass falls a vertical distance L/2, so the loss in gravitational potential energy is MgL/2. Equating this to rotational kinetic energy 1/2 Iω² with I = ML²/3 gives ω² = 3g/L.

Question 40Physics

An electron is confined in a one-dimensional infinite square well of width L. What is the energy of the photon emitted when the electron makes a transition from the n = 2 state to the n = 1 state?

  1. h²/(8mL²)
  2. h²/(2mL²)
  3. 3h²/(2mL²)
  4. 3h²/(8mL²) Correct answer.

Explanation

The energy levels of an infinite square well are E_n = n²h²/(8mL²). The transition from n = 2 to n = 1 releases ΔE = (4 − 1)h²/(8mL²) = 3h²/(8mL²), which is the photon energy.

Question 41Physics

The SI unit of magnetic flux is the

  1. tesla
  2. henry
  3. weber Correct answer.
  4. farad

Explanation

Magnetic flux is defined as the product of magnetic flux density and area, Φ = B·A, so its unit is T·m², which is called the weber. The tesla is the unit of flux density, the henry is the unit of inductance, and the farad is the unit of capacitance.

Question 42Physics

A particle moves in a horizontal circle at constant speed. Which quantity remains constant during the motion?

  1. Acceleration
  2. Linear momentum
  3. Velocity
  4. Kinetic energy Correct answer.

Explanation

Kinetic energy depends on the square of speed, so it stays constant when the speed is constant. Velocity, acceleration, and linear momentum are vectors whose directions change continuously as the particle goes around the circle.

Question 43Physics

The work done by a conservative force on a particle that moves around any closed path is

  1. path-dependent
  2. negative
  3. positive
  4. zero Correct answer.

Explanation

For a conservative force, the work done depends only on the initial and final positions, not on the path taken. When the initial and final positions are the same, as in a closed path, the net work is therefore zero.

Question 44Physics

A projectile is launched from level ground with speed 20 m/s at 30° above the horizontal. Taking g = 10 m/s² and neglecting air resistance, what maximum height does it reach?

  1. 20 m
  2. 10 m
  3. 15 m
  4. 5 m Correct answer.

Explanation

The vertical component of the launch velocity is v_y = 20 sin 30° = 10 m/s. At maximum height the vertical velocity is zero, so h = v_y²/(2g) = 10²/(2×10) = 5 m.

Question 45Physics

Two point charges of +4.0 μC and +1.0 μC are separated by 0.30 m in vacuum. Taking k = 9.0×10^9 N·m²/C², what is the magnitude of the electrostatic force between them?

  1. 0.40 N Correct answer.
  2. 4.0 N
  3. 0.80 N
  4. 0.20 N

Explanation

Coulomb's law gives F = k|q₁q₂|/r². Substituting the values, F = (9.0×10^9)(4.0×10^-6)(1.0×10^-6)/(0.30)² = 0.40 N.

Question 46Physics

In a process, 200 J of heat is added to a gas and the gas does 80 J of work on its surroundings. What is the change in internal energy of the gas?

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

Explanation

The first law of thermodynamics gives ΔU = Q − W, where Q is heat added to the gas and W is work done by the gas. Thus ΔU = 200 J − 80 J = 120 J.

Question 47Physics

An inductor of inductance 0.10 H is connected to an AC source of frequency 50 Hz. What is its inductive reactance? (Take π = 3.14)

  1. 15.7 Ω
  2. 3.14 Ω
  3. 314 Ω
  4. 31.4 Ω Correct answer.

Explanation

Inductive reactance is given by X_L = 2πfL. Substituting f = 50 Hz and L = 0.10 H gives X_L = 2 × 3.14 × 50 × 0.10 = 31.4 Ω.

Question 48Physics

In a Young's double-slit experiment, the slit separation is 1.0 mm, the screen distance is 1.0 m, and the light wavelength is 600 nm. What is the fringe spacing on the screen?

  1. 6.0 mm
  2. 0.60 mm Correct answer.
  3. 1.2 mm
  4. 0.30 mm

Explanation

Fringe spacing for Young's double slit is Δy = λD/d. Using λ = 600 nm = 6.0×10^-7 m, D = 1.0 m, and d = 1.0×10^-3 m gives Δy = 6.0×10^-4 m = 0.60 mm.

Question 49Physics

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

  1. 3.10 eV
  2. 1.24 eV
  3. 0.62 eV Correct answer.
  4. 2.48 eV

Explanation

The photon energy is hc/λ = 1240/400 = 3.10 eV, and the work function is hc/λ₀ = 1240/500 = 2.48 eV. The maximum kinetic energy is the difference, 3.10 − 2.48 = 0.62 eV.

Question 50Physics

A point charge q is placed at the centre of a cube of side a. What is the electric flux through one face of the cube?

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

Explanation

By Gauss's law, the total electric flux through the closed cube is q/ε₀. Because the charge is at the centre and the cube has six identical faces, the flux through one face is one-sixth of the total, q/(6ε₀).