A simple pendulum oscillates in a vertical plane. When it passes through the mean position, the tension in the string is $3$ times the weight of the pendulum bob. What is the maximum displacement of the pendulum of the string with respect to the vertical ……… $^o$.

A simple pendulum is released from $A$ as shown in figure. If $m$ and $l$ represent the mass of the $bob$ and the length of the pendulum respectively, the gain in kinetic energy at $B$ is

A bob of mass mis suspended by a light string of length $L$. It is imparted a horizontal velocity $v_{o}$ at the lowest point $A$ such that it completes a semi-circular trajectory in the vertical plane with the string becoming slack only on reaching the topmost point, C. This is shown in Figure Obtain an expression for $(i)\;v_{o} ; (ii)$ the speeds at points $B$ and $C ;(iii)$ the ratio of the kinetic energles $\left(K_{B} / K_{C}\right)$ at $B$ and $C$. Comment on the nature of the trajectory of the bob after it reaches the point $C$

A body of mass $1\, kg$ is moving in a vertical circular path of radius $1\,m$. The difference between the kinetic energies at its highest and lowest position is ……… $J$