Mass m₁ moves on a slope making an angle θ with the horizontal and is attached to mass m₂ by a string passing over a frictionless pulley as shown in Fig. The co-efficient of friction between m₁ and the sloping surface is µ. Which of the following statements are true?

(a) If m₂ > m₁ sin θ , the body will move up the plane.

(b) If m₂ > m₁ (sin θ + µcos θ) , the body will move up the plane.

(c) If m₂ < m₁ (sin θ + µcos θ) , the body will move up the plane.

(d) If m₂ < m₁ (sin θ - µcos θ) , the body will move down the plane..

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