Physics - W.E.P. Question with Solution | TestHub

Let $\omega$ be the angular velocity of the stone. Since the stone makes $n$ revolutions per minute, the angular velocity in radians per second is given by

$\omega =\frac{2\pi n}{60}=\frac{\pi n}{30}$

At the lowest point of the vertical circle, the forces acting on the stone are the tension $T$ in the string directed upwards towards the center and the weight $mg$ directed downwards. The net force provides the necessary centripetal acceleration:

$T-mg=m{\omega }^{2}r$

Substituting the value of $\omega$, we get

$T=mg+m{\left(\frac{\pi n}{30}\right)}^{2}r$

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

Answer: $m\left[g+\frac{{\pi }^2{n}^{2}r}{900}\right]$