A particle connected to the end of a spring executes S.H.M. with period '$$T_1$$'. While the corresponding period for another spring is '$$\mathrm{T}_2$$'. If the period of oscillation with two springs in series is 'T', then

The change in internal energy of the mass of a gas, when the volume changes from '$$\mathrm{V}$$' to '$$2 \mathrm{~V}$$' at constant pressure 'P' is ($$\gamma=$$ Ratio of Cp to Cv)

An object is located on a wall, its image of equal size is to be obtained on a parallel wall with the help of a convex lens. The lens is placed at a distance '$$\mathrm{d}$$' in front of the second wall. The required focal length of the lens is

A child is standing with folded hands at the centre of the 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 double. The kinetic energy of the system now is