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A particle is executing simple harmonic motion with a time period T. At time t = 0, it is at its position of equilibrium. The kinetic energy-time graph of the particle will look like:

Answer: (4) KE = (1 / 2) mω2A2cos2 ωt... View Article

The temperature of an open room of volume 30 m³ increases from 17^oC to 27^oC due to the sunshine. The atmospheric pressure in the room remains 1 × 10⁵ Pa. If n_i and n_fare the number of molecules in the room before and after heating, then n_f− n_i will be:

1) −1.61 × 1023 2) 1.38 × 1023 3) 2.5 × 1025 4) −2.5 × 1025 Answer: (4) n1 = initial number of moles n1 = P1V1 / RT1 = (105 * 30) / (8.3... View Article

C_p and C_v are specific heats at constant pressure and constant volume respectively. It is observed that

Cp − Cv = a for hydrogen gas Cp − Cv = b for nitrogen gas The correct relation between a and b is : 1) a = 1 / 14 b 2) a = b 3) a = 14 b 4)... View Article

An external pressure P is applied on a cube at 0°C so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and ɑ is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by :

1) P / 3ɑK 2) P / ɑK 3) 3ɑ / PK 4) 3PKɑ Answer: (1) K = ΔP / (-ΔV / V) ΔV / V = P / K V = Vo (1 + γ Δt) ΔV / Vo = γ Δt P / K = γ Δt... View Article

A copper ball of mass 100 gm is at a temperature T. It is dropped in a copper calorimeter of mass 100 gm, filled with 170 gm of water at room temperature. Subsequently, the temperature of the system is found to be 75⁰C. T is given by : (Given : room temperature = 30⁰C, specific heat of copper = 0.1 cal / gm^oC)

1) 800oC 2) 885oC 3) 1250oC 4) 825oC Answer: (2) 100 × 0.1 × (t – 75) = 100 × 0.1 × 45 + 170 × 1 × 45 10t – 750 = 450 + 7650 10t = 1200... View Article

The variation of acceleration due to gravity g with distance d from the centre of the earth is best represented by (R = Earth’s radius):

Answer: (4) Variation of g inside earth surface d < R = g = [Gm / R2] * d d = R = gs = Gm / R2 d > R = g = Gm / d2... View Article

A slender uniform rod of mass M and length l is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle θ with the vertical is:

1) [3g / 2l] sin θ 2) [2g / 3l] sin θ 3) [3g / 2l] cos θ 4) [2g / 3l] cos θ Answer: (1) Torque at angle θ τ = Mg sin θ (l / 2) τ... View Article

The moment of inertia of a uniform cylinder of length l and radius R about its perpendicular bisector is I. What is the ratio l / R such that the moment of inertia is minimum?

1) √(3 / 2) 2) √3 / 2 3) 1 4) 3 / √2 Answer: (1)... View Article

A time-dependent force F = 6t acts on a particle of mass 1 kg. If the particle starts from rest, the work done by the force during the first 1 sec. will be:

1) 4.5 J 2) 22 J 3) 9 J 4) 18 J Answer: (1) 6t = 1 * (dv / dt) ∫0v dv = ∫6t dt v = 6 [t2 / 2]01 = 3 ms-1 W = ΔKE = (1 / 2) (1) (9)... View Article

A body of mass m = 10⁻² kg is moving in a medium and experiences a frictional force F = −kv². Its initial speed is v₀= 10 ms⁻¹. If, after 10 s, its energy is 1 / 8 mv₀2, the value of k will be:

1) 10−3 kg m−1 2) 10−3 kg s−1 3) 10−4 kg m−1 4) 10−1 kg m−1 s−1 Answer: (3) kf / ki = (1 / 8) mvo2 / (1 / 2) mvo2 = 1 / 4 vf / vi = 1 / 2... View Article

A body is thrown vertically upwards. Which one of the following graphs correctly represents the velocity vs time?

Answer: (3) Acceleration is constant and negative.... View Article

A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains the same, the stress in the leg will change by a factor of:

1) 9 2) 1 / 9 3) 81 4) 1 / 81 Answer: (1) vf / vi = 93 ∵ Density remains same So, mass ∝ Volume mf / mi = 93 (Area)f / (Area)i = 92... View Article

A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the nth power of R. If the period of rotation of the particle is T, then:

a. T ∝ R(n+1)/2 b. T ∝ R n/2 c. T ∝ R n/2 for any n d. T ∝ R(n/2)+1 Answer: (a) T ∝ R(n+1)/2... View Article

two moles of an ideal monoatomic gas occupies a volume v at 27 degrees

(1) (a) 189 K (b) -2.7 kJ (2) (a) 195 K (b) 2.7 kJ (3) (a) 189 K (b) 2.7 kJ (4) (a) 195 K (b) -2.7 kJ Answer: (1) ΔU = -2.76 kJ... View Article

All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.

Answer: (4) If Vs t is a straight line with -ve slope acc = - ve const. Displacement Vs time is a parabola opening downward Only incorrect... View Article

In an a.c. circuit, the instantaneous e.m.f. and current are given by e = 100 sin 30 t and i = 20 sin(30 t – (π/4)). In one cycle of a.c., the average power consumed by the circuit and the wattles current are, respectively:

a. ((50/√2),0) b. 50,0 c. 50,10 d. ((1000//√2),10) Answer: (d)... View Article

On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10 cm. The resistance of their series combination is 1 k Ω. How much was the resistance on the left slot before interchanging the resistances?

a. 550 Ω b. 910 Ω c. 990 Ω d. 505 Ω Answer: (a) Let balancing length be L --------(1) If R1 and R2 are interchanged balancing length is... View Article

The density of the material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the density is:

a. 4.5 % b. 6 % c. 2.5 % d. 3.5 % Answer: (a) = 1.5 + 3 x 1 = 4.5... View Article

The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is B₁. When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is B₂. The ratio B₁/B₂ is:

a. √2 b. 1/√2 c. 2 d. √3 Answer: (a) Dipole moment μ = niA μ = ix πR2 If dipole moment is doubled keeping current const. R2 = R1√2... View Article

Caspian Sea

The Caspian Sea is the world's largest inland body of water, variously classed as the world's largest lake or a full-fledged sea. An endorheic... View Article