Question

A stone of mass $m$ is tied to a string and is moved in a vertical circle of radius $r$ making n rev/min. The total tension in the string when the stone is at the lowest point is

• A. mg
• B. $m(g + \pi nr^2)$
• C. m(g + nr)
• D. $m\begin{Bmatrix}g+\frac{\pi^2n^2r}{900}\end{Bmatrix}$

Answer 1

Answer: (D)

$m\begin{Bmatrix}g+\frac{\pi^2n^2r}{900}\end{Bmatrix}$

Answer 2

$T_{net} = \frac{m\nu^2}{r} + mg = mr\omega^2 + mg$ = $mr\left(\frac{2\pi n }{60}\right)^2 +mg$ = $m \left[\frac{\pi^2n^2r}{900} + g\right]$