$A$ particle tied to one end of a string is being rotated in a vertical circle with constant frequency. The tension in the string at points $A, B, C$ and $D$ are $T_1, T_2, T_3$ and $T_4$ respectively. Then:

Length of a simple pendulum is $1 \,m$. When its bob is at its lowest point its velocity is $7 \,ms^{-1}$. If the bob leaves its circular path at a height $h$ above the centre of the circle, then the value of $h$ is $(g=10 \,ms^{-2})$. (in $\,m$)

$A$ bob of mass $m$ is suspended at a point $O$ by a light string of length $l$ and is set to perform vertical circular motion as shown in the figure. Initially,by applying a horizontal velocity $v_0$ at point $A$,the string becomes slack when the bob reaches point $D$. The ratio of the kinetic energy of the bob at points $B$ and $C$ is:

$A$ 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 ....... $m/s$.

$A$ mass $m$ is released from point $A$ as shown in the figure. The tension in the string at point $B$ will be:

Concrete mixture is made by mixing cement,stone,and sand in a rotating cylindrical drum. If the drum rotates too fast,the ingredients remain stuck to the wall of the drum and proper mixing of ingredients does not take place. The maximum rotational speed of the drum in revolutions per minute (rpm) to ensure proper mixing is close to (Take the radius of the drum to be $1.25\, m$ and its axle to be horizontal).