A boat crosses a river from one bank A to another bank B which is opposite. The distance between them is D. The speed of water is $V_W$ and that of boat relative to water is $V_B$. If $V_B = 2V_W$, the time taken by the boat to cross the river directly along AB is $\left(\sin 30^\circ = \dfrac{1}{2}\right)$, $\left(\cos 30^\circ = \dfrac{\sqrt{3}}{2}\right)$

The weight of man in lift moving in upward direction with an acceleration 'a' is $660$ N. When the lift moves in the downward direction with the same acceleration, his weight is found to be $380$ N. The real weight of the man when the lift is at rest is

A solid sphere rolls down from the top of an inclined plane. On reaching the bottom of the plane, its velocity is '$V_1$'. When the same sphere slides down from the top of the same plane of same height, its velocity on reaching the bottom is '$V_2$'. The ratio $V_1 : V_2$ is (neglect friction)

Two identical rings A and B of same mass and radius are revolving, ring A arounds its own diameter and ring B about tangential axis in its own plane. Both the rings A and B have same rotational kinetic energy. The ratio of the angular velocity of ring B to that of ring A is