Question

A particle of mass $m$ is being circulated on a vertical circle of radius $r$. If the speed of particle at the highest point be $v$, then:

• A. $mg=\frac{{mv}^2}{r}$
• B. $mg\ge \frac{{mv}^2}{r}$
• C. $mg<\frac{{mv}^2}{r}$
• D. None of these

Answer 1

The correct option is C $mg<\frac{{mv}^2}{r}$

At the highest point $m{v}^2/r$ is the centripetal force on the particle which keeps it in circular motion and $mg$ is the force of gravity on the particle. If the particle should remain in circular motion and not become slack at the highest point then $mg<\frac{m{v}^2}{r}$