A kathak dancer is standing on horizontal surface with folded hands. In the begining dancer is rotating about his central axis and his kinetic energy is 'K' at that time. The kathak dancer now stretches his arms so that the moment of inertia of the dancer becomes three times and the angular velocity becomes one-third. The kinetic energy of the dancer now is

A solid sphere rolls without slipping on an inclied plane at an angle $\theta$. The ratio of total kinetic energy to its rotational kinetic energy is

The acceleration due to gravity at a height 'h' above the surface of earth is '$g_h$'. At the depth 90 km below the earth's surface the acceleration due to gravity is also '$g_h$'. The value of 'h' is

An incompressible fluid (ideal fluid) is flowing through non uniform cross-sectional tube PQ as shown in the figure from end P to end Q. If $K_P$ and $K_Q$ are the kinetic energy per unit volume of the fluid at end P and end Q respectively, then