A vernier calliper whose 10 vernier scale divisions coincide with 9 main scale divisions is used to take a reading. Each main scale division is 1 mm. Before taking the reading it is observed that the 4^th division of the vernier scale coincides with the main scale and zero of main scale is behind zero of vernier scale. When the reading is taken using this vernier calliper, the main scale reads 2.5 cm and the 7^th division of the vernier scale coincides with the main scale. Find the final value of the measurement.

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