Question

A stone of mass m is tied to a string and is moved in a vertical circle of radius R making f revolutions per minute. The total tension in the string when the stone is at its lowest point is

• A. $m(g+f^2{R}^2)$
• B. $m(g+\pi f{R}^2)$
• C. $m(g+\pi fR)$
• D. $m\left\{\frac{g+\left({\pi }^2{f}^{2}R\right)}{900}\right\}$

Answer 1

The correct option is D $m\left\{\frac{g+\left({\pi }^2{f}^{2}R\right)}{900}\right\}$

Tension at lowest point $T=mg+m{\omega }^{2}R=mg+m4{\pi }^2{f}^{2}R$
If n is revolution per minute then $T=mg+m4{\pi }^2\frac{f^2}{3600}R=mg+\frac{m{\pi }^2{f}^{2}R}{900}$