Q. A stone of mass $m$ is tied to a string and is moved in a vertical circle of radius $r$ making $n$ revolutions per $minute.$ The total tension in the string when the stone is at its lowest point is
A) $mg$
B) $m(g + \pi nr^{2})$
C) $m(g + \pi nr)$
D) $m\left\{ g + (\pi^{2}\ n^{2}\ r)/900 \right\}$
Explanation
(d) $T = mg + m\omega^{2}r = m\left\{ g + 4\pi^{2}n^{2}r \right\}$
$= m\left\{ g + \left( 4\pi^{2}\left( \frac{n}{60} \right)^{2}r \right) \right\} = m\left\{ g + \left( \frac{\pi^{2}n^{2}r}{900} \right) \right\}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.