A stone of mass m is tied to a string and is moved in a vertical circle of radius r making n r

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5.Work, Energy, Power and Collision

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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

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

C

$m(g + \pi \,n\,r)$

D

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

Solution

(d) $T = mg + m{\omega ^2}r = m\{ g + 4{\pi ^2}{n^2}r\} $

$ = m\left\{ {g + \left( {4{\pi ^2}{{\left( {\frac{n}{{60}}} \right)}^2}r} \right)} \right\} $

$= m\left\{ {g + \left( {\frac{{{\pi ^2}{n^2}r}}{{900}}} \right)} \right\}$

Standard 11

Physics

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