The maximum value attained by the tension in the string of a swinging pendulum is four times the minimum value it attains. There is no slack in the string. The angular amplitude of the pendulum is (in $^{\circ}$)

$A$ 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

$A$ stone of mass $150 \ g$ moves in a vertical circle at the end of a string. The radius of the circle is $70 \ cm$ and the speed of the stone at the topmost point $P$ is $3.5 \ m/s$. For the instant at which the stone passes through the highest point $P$,the centripetal force is nearly ......... $N$ (take $g = 10 \ m/s^2$).

In the figure shown,a particle is released from the position $A$ on a smooth track. When the particle reaches at $B$,then the normal reaction on it by the track is .........

$A$ point mass '$m$' attached at one end of a massless,inextensible string of length '$\ell$' performs a vertical circular motion and the string rotates in a vertical plane,as shown in the diagram. The increase in the centripetal acceleration of the point mass when it moves from point $A$ to point $C$ is $(g = \text{acceleration due to gravity})$:

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).