In Fig , a body A of mass m slides on plane inclined at angle θ1 to the horizontal and µ1 is the coefficient of friction between A and the plane. A is connected by a light string passing over a frictionless pulley to another body B, also of mass m, sliding on a frictionless plane inclined at angle θ2 to the horizontal. Which of the following statements are true?

(a) A will never move up the plane.

(b) A will just start moving up the plane when µ= $\frac{\mathit{s}\mathit{i}\mathit{n}{\mathit{\theta }}_2-\mathit{s}\mathit{i}\mathit{n}{\mathit{\theta }}_1}{\mathit{c}\mathit{o}\mathit{s}{\mathit{\theta }}_1}$  .

(c) For A to move up the plane, θ₂ must always be greater than θ₁ .

(d) B will always slide down with constant speed.

Two SHMs in same direction are represented by y1 = asinωt and y2 = asin(ωt + δ). When they superimpose, the initial phase difference of the resultant SHM is

The potential energy of a particle of mass 2 kg in motion along the x-axis is given by U = 2 (1 – cos 2x) J, where x is in meters. The period of small oscillations (in s) is

A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is K. The child now stretches his arms so that the moment of inertia of the system becomes 3/2 of the initial moment of inertia. The kinetic energy of the system is now

If the absolute temperature of hot black body is raised by 2%, by how much percentage rate of heat energy radiated would be increased nearly?

Two moles of helium gas are taken over the cycle ABCDA as shown below in P-T diagram. Assuming the gas to be ideal, the work done on the gas in taking from A to B is