$A$ mass $m$ is attached to a string and revolves in a vertical circle. What is the tension in the string when the mass is at the lowest position?

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).

$A$ bullet of mass $m$ and velocity $v$ strikes the bob of a pendulum of mass $M$ and emerges out with velocity $v/2$. What is the minimum value of $v$ such that the bob of the pendulum will swing through a complete circle? (Take the length of the pendulum $= \ell$)

$A$ particle originally at rest at the highest point of a smooth vertical circle is slightly displaced. It will leave the circle at a vertical distance $h$ below the highest point,such that

$A$ 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:

$A$ particle of mass $100 \ g$ is performing vertical circular motion as shown in the figure. Find the tangential acceleration at the given position in $m/s^2$. (Take $g = 10 \ m/s^2$)