The string of a pendulum of length $l$ is displaced through $90^{\circ}$ from the vertical and released. The minimum strength of the string required to withstand the tension as the pendulum passes through the mean position is:

$A$ body crosses the topmost point of a vertical circle with critical speed. Its centripetal acceleration,when the string is horizontal,will be

$A$ small sphere is moving at a constant speed in a vertical circle. Below is a list of quantities that could be used to describe some aspect of the motion of the sphere.
$I$ - Kinetic energy
$II$ - Gravitational potential energy
$III$ - Momentum
Which of these quantities will change as this sphere moves around the circle?

$A$ hollow sphere has a radius of $6.4 \, m$. The minimum velocity required by a motorcyclist at the bottom to complete the vertical circle is ........... $m/s$.

$A$ particle of mass $m$ is released from a height $H$ on a smooth curved surface which ends into a vertical loop of radius $R$,as shown. Choose the correct alternative$(s)$ if $H = 2R$.

$A$ bob of mass $M$ is suspended by a massless string of length $L$. The horizontal velocity $V$ at position $A$ is just sufficient to make it reach the point $B$. The angle $\theta$ at which the speed of the bob is half of that at $A$, satisfies: