$A$ body of mass $2 \, kg$ is tied to a string of length $2 \, m$ and rotated in a vertical circle. What is the difference between the maximum and minimum kinetic energy in $J$?

The mass of the bob of a simple pendulum of length $L$ is $m$. If the bob is released from its horizontal position,then the speed of the bob and the tension in the thread at the lowest position of the bob will be respectively:

$A$ particle originally at rest at the highest point of a smooth vertical circle (radius $R = 1.8 \ m$) is slightly displaced. It will leave the circle at a vertical distance $h$ from the bottom. The value of $h$ will be ..... $m$.

$A$ 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. The minimum value of $H$ required so that the particle makes a complete vertical circle is given by (in $R$)

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