Question

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. $m\{ g + (\pi^{2}n^{2}r)/900\}$
• B. $m(g + \pi nr^{2})$
• C. $m(g + \pi nr)$
• D. $m(g + n^{2}r^{2})$

Answer 1

Answer: (A)

$m\{ g + (\pi^{2}n^{2}r)/900\}$

Answer 2

Tension at lowest point $T = mg + mw^{2}r$

$= mg + m4\pi^{2}n^{2}r$

If n is revolution per minute then $T = mg + m4\pi^{2}\frac{n^{2}}{3600}r = mg + \frac{m\pi^{2}n^{2}r}{900} = m\left\lbrack g + \frac{\pi^{2}n^{2}r}{900} \right\rbrack$