The least count of the main scale of a vernier callipers is 1 mm. Its vernier scale is divided into 10 divisions and coincide with 9 divisions of the main scale. When jaws are touching each other, the 7th division of vernier scale coincides with a division of main scale and the zero of vernier scale is lying right side of the zero of main scale. When this vernier is used to measure length of cylinder the zero of the vernier scale is between 3.1 cm and 3.2 cm and 4th VSD coincides with a main scale division. The length of the cylinder is (VSD is vernier scale division)

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