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

The tension at the lowest point is given by

$T_1 = \frac{m}{r}(v^2+gr)$

        = $m(\frac{v^2}{r}+g)$

       = $m(\frac{r^2{\omega }^2}{r}+g)(v = r\omega )$------(i)

Now $\omega = 2\mathrm{\pi f}$ where f = frequency of revolution. The frequeny of revolution per sec, n = $\left(\frac{f}{60}\right)$

$\omega = 2 \mathrm{\pi n}/60 = \left(\frac{\mathrm{\pi n}}{30}\right)-----\left(\mathrm{ii}\right)$

From equation (i) and (ii),    $T_1 = m[\frac{r^2{\mathrm{\pi }}^2{\mathrm{n}}^2}{900r}+g]$    

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