Answer to Question #141540 in Mechanics | Relativity for Gady

Question

When a stone of mass m at the end of a string is whirled in a vertical circle at a constant speed, (A) the tension (force) in the string stays constant (B) the tension is least when the stone reaches the bottom of the circle (C) the tension in the string is always mg (D) the weight mg is always the centripetal force (E) the tension is greatest when the stone is at the bottom of the circle

Answer 1

Equation of motion in vertical circular motion can be given as

$T-mgcos\theta=\frac{mv^2}{r}$

$T=\frac{mv^2}{r}+mgcos\theta$

Where $\theta$ is angle of string with the vertical axis.

At bottom of circle $\theta=0°$

So

$T=\frac{mv^2}{r}+mg$

So tension will be maximum

(E) the tension is greatest when the stone is at the bottom of the circle.

Is the correct statement.