As per given figure to complete the circular loop what should be the radius if initial height is $5 \,m$ ………. $m$.

A stone tied to a string of length $L$ is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed $u$. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is

The tube $AC$ forms a quarter circle in a vertical plane. The ball $B$ has an area of cross-section slightly smaller than that of the tube, and can move without friction through it. $B$ is placed at $A$ and displaced slightly. It will

$A$ 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 If $\theta$ is instantaneous angle which the line joining the particle and the centre of the loop makes with the vertical, then identify the correct statement $(s)$ related to the normal reaction $N$ between the block and the surface

The bob of a simple pendulum is displaced from its equilibrium position $O$ to a position $Q$ which is at height $h$ above $O$ and the bob is then released. Assuming the mass of the bob to be $m$ and time period of oscillations to be $2.0\  s$, the tension in the string when the bob passes through $O$ is