$A$ mass attached to one end of a string crosses the topmost point on a vertical circle with critical speed. Its centripetal acceleration when the string becomes horizontal will be ($g =$ gravitational acceleration).

$A$ bucket filled with water is tied to a rope of length $0.5 \,m$ and is rotated in a circular path in a vertical plane. The minimum velocity it should have at the lowest point of the circle so that the water does not spill is, $(g=10 \,m/s^2)$

$A$ particle is moving along a vertical circle of radius $R$. At point $P$,what will be the velocity of the particle? (Assume the critical condition at the highest point $C$).

$A$ fighter plane is moving in a vertical circle of radius $r$. Its minimum velocity at the highest point of the circle will be

The maximum value attained by the tension in the string of a swinging pendulum is four times the minimum value it attains. There is no slack in the string. The angular amplitude of the pendulum is (in $^{\circ}$)

If a particle completes a vertical circular motion,what is the ratio of its velocities at points $A$,$B$,and $C$?