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A thin lens made of glass (refractive index 1.5) of focal length f = 16 cm is immersed in a liquid of refractive index 1.42. If its focal length in liquid is fi, then the ratio f_l/ f is closest to the integer

a. 9 b. 17 c. 1 d. 5 Answer: (a) = f1/fa = 1.42×0.5/0.08 = 8.875 = 9... View Article

A planar loop of wire rotates in a uniform magnetic field. Initially at t = 0, the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of 10 s about an axis in its plane, then the magnitude of induced emf will be maximum and minimum, respectively at

a. 2.5 sec and 5 sec b. 5 sec and 7.5 sec c. 2.5 sec and 7.5 sec d. 5 sec and 10 sec Answer: (a) ω = 2π/T = π/5 when ωt = π/2 Then φflux... View Article

An electron (of mass m) and a photon have the same energy E in the range of few eV. The ratio of the de Broglie wavelength associated with the electron and the wavelength of the photon is. ( c = speed of light in vacuum)

a. (E/2m)1/2 b. 1/c (2E/m)1/2 c. c(2mE)1/2 d. 1/c (E/2m)1/2 Answer: (d) λd for electron = h/√(2me) λp for photon = hc/E Ratio = [h/√(2me)... View Article

A stationary observer receives sound from two identical tuning forks, one of which approaches and the other one receded with the same speed (much less than the speed of sound). The observer hears 2 beats/sec. The oscillation frequency of each tuning fork is v₀= 1400 Hz and the velocity of sound in air is 350 m/s. The speed of each tuning fork is close to

a. 1/4 m/s b. 1 m/s c. 1/2 m/s d. 1/8 m/s Answer: (a) f0 C/(C-V)- f0C/(C+V)= 2 V = ¼ m/s... View Article

A particle of mass m and charge q has an initial velocity [latex]vec{v} = v_{0}: hat{j}[/latex]. If an electric field [latex]vec{E} = E_{0}: hat{i}[/latex] and magnetic field [latex]vec{B} = B_{0}: hat{i}[/latex] act on the particle, its speed will double after a time

a. √3mv0/qE0 b. √2mv0/qE0 c. 3mv0/qE0 d. 2mv0/qE0 Answer: (a) Magnetic field can only change direction of speed as it cannot do any work.... View Article

In the figure, potential difference between a and b is

a. 0 V b. 15 V c. 10 V d. 5 V Answer: (c) Diode is in forward bias, so it will behave as simple wire. So, the circuit effectively... View Article

An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are 6.4 cm and 4.8 cm, respectively. The ratio of minimum and maximum velocities of fluid in this pipe is

a. √(3/2) b. 9/16 c. 3/4 d. √3/4 Answer: (b) Given, Maximum diameter of pipe = 6.4 Minimum diameter of pipe = 4.8 Using equation of... View Article

The activity of a radioactive substance falls from 700 s^-1 to 500 s^-1 in 30 minutes. Its half life is close to

a. 66 min b. 62 min c. 52 min d. 72 min Answer: (b) Using the half-life equation ln A0/At = λt At half life, t = λt1/2 and At = A0/2 ln 2... View Article

Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperatures T₁ and T₂. The temperature of the hot reservoir of the first engine is T₁ and the temperature of the cold reservoir of the second engine is T₂. T is the temperature of the sink of first engine which is also the source for the second engine. How is T related to T₁ and T₂ if both the engines perform equal amount of work?

a. T = 2T1T2/(T1+T2) b. T = (T1+T2)/2 c. T = 0 d. T = √T1T2 Answer: (b) Heat input to 1st engine = QH Heat rejected from 1st engine= Q... View Article

Mass per unit area of a circular disc of radius a depends on the distance r from its centre as σ(r) = A + Br. The moment of inertia of the disc about the axis, perpendicular to the plane and passing through its centre is

a. b. c. d. Answer: (a) = A + Br ∫dm = ∫(A+Br) 2πrdr I = ∫dm r2 = ∫0a(A+Br)2πr3dr = 2 π(A (a4/4) + B(a5/5)) = 2π a4 (A/4) + Ba/5)... View Article

A mass of 10 kg is suspended by a rope of length 4 m, from the ceiling. A force F is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of 45° with the vertical. Then F equals (Take g = 10 m/s² and rope to be massless)

a. 100 N b. 90 N c. 75 N d. 70 N Answer: (a) Equating the vertical and horizontal components of the forces acting at point T/√2 = 100... View Article

Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently, the mean collision time between the gas molecules changes from τ₁ to τ₂. If C_p/C_v = γ for this gas, then a good estimate for τ₂ /τ₁is given by

a. 1/2 b. (1/2) (γ +1)/2 c. (1/2) γ d. 2 Answer: (b) Relaxation time (τ) dependence on volume and temperature can be given by τ ∝ V/√T.... View Article

In a building, there are 15 bulbs of 45 W, 15 bulbs of 100 W, 15 small fans of and 2 heaters of 1kW. The voltage of electric main is 220V. The minimum fuse capacity (rated value) of the building will be approximately

a. 10 A b. 20 A c. 25 A d. 15 A Answer: (b) Total power consumption of the house (P) = Number of appliances ×Power rating of each appliance... View Article

A box weighs 196 N on a spring balance at the North Pole. Its weight recorded on the same balance if it is shifted to the equator is close to (Take g = 10m/s² at the North Pole and radius of the Earth = 6400 km )

a. 194.32 N b. 194.66 N c. 195.32 N d. 195.66 N Answer: (c) Weight of the object at the pole,W = mg = 196 N Mass of the object, m = w/g =... View Article

Five equal forces of 10 N each are applied at one point and all are lying in one plane. If the angles between them are equal, the resultant force will be

1) Zero 2) 10 N 3) 20 N 4) 10√2 N Answer: 1) Zero Solution: If the angle between all forces which are equal and lying in... View Article

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