$A$ mass attached to one end of a string crosses the topmost point on a vertical circle with critical speed. Its centripetal acceleration when the string becomes horizontal will be ($g =$ gravitational acceleration).

$A$ stone of mass $1\, kg$ tied to a light inextensible string of length $L = \frac{10}{3}\, m$ is whirling in a circular path of radius $L$ in a vertical plane. If the ratio of the maximum tension in the string to the minimum tension in the string is $4$ and if $g$ is taken to be $10\, m/s^2$,the speed of the stone at the highest point of the circle is ....... $m/s$.

$A$ $1\, kg$ stone at the end of a $1\, m$ long string is whirled in a vertical circle at a constant speed of $4\, m/s$. The tension in the string is $6\, N$ when the stone is at $(g = 10\, m/s^2)$.

$A$ block of mass $m$ is given a velocity $20\ m/s$ on a horizontal rough surface of length $x\ m$. After the rough surface,there is a vertical circular path of radius $R = 2\ m$ which is frictionless. The block enters the circular path with the minimum velocity required to complete the path. Find the length of the rough surface $x$ if the coefficient of friction is $\mu = 0.5$.

$A$ simple pendulum of length $L$ carries a bob of mass $m$. When the bob is at its lowest position, it is given the minimum horizontal speed necessary for it to move in a vertical circle about the point of suspension. When the string is horizontal, the net force on the bob is

$A$ fighter plane is moving in a vertical circle of radius $r$. Its minimum velocity at the highest point of the circle will be