$A$ body of mass $m$ is tied to a string of length $l$ and rotated in a vertical circle. What is the difference in tension between the lowest point and the highest point (in $,mg$)?

$A$ car starts from rest at height $H$ and moves along a track to complete a vertical loop of radius $r$. If the car just completes the loop,find the ratio $H/h$,where $h$ is the height of the loop above the starting point of the loop track.

$A$ weightless thread can support a tension of up to $30 \, N$. $A$ stone of mass $0.5 \, kg$ is tied to it and is revolved in a circular path of radius $2 \, m$ in a vertical plane. If $g = 10 \, m/s^2$,then the maximum angular velocity of the stone will be ........ $rad/s$.

$A$ rod of length $L$ is hung from one of its ends,and a mass $m$ is attached to its free end. What tangential velocity must be imparted to $m$ so that it reaches the top of the vertical circle? ($g$ = acceleration due to gravity)

$A$ mass is performing vertical circular motion (see figure). If the average velocity of the particle is increased,then at which point will the string break?

$A$ small sphere of mass $m$ is suspended by a light and inextensible string of length $l$ from a point $O$ fixed on a smooth inclined plane of inclination $\theta$ with the horizontal. The sphere is moving in a circle on the incline as shown. If the sphere has a velocity $u$ at the top most position $A$, then: