Question

A ball of mass $m$ is tied up with string and rotated along a horizontal circle of radius $r$. At an instant, its velocity is $v$, and tension in string is $T$. The force required for circular motion is:

• A. $T-\frac{m{v}^2}{r}$
• B. $T+\frac{m{v}^2}{r}$
• C. $\frac{m{v}^2}{r}$
• D. Zero

Answer 1

Answer: (C)

$\frac{m{v}^2}{r}$

Let the string make an angle $\theta$ to the normal at the point of suspension. The horizontal component of tension provides the necessary centripetal force.

Therefore, $T\sin \theta =\frac{m{v}^2}{r}$.