Question

A particle is moving in a vertical circle such that the tension in the string at the topmost point is zero. What is the acceleration of the particle at point bottommost point?

(g = 10 $m/s^2$)

Answer 1

$T+mg=\frac{m{u}^2}{r}butT=0\frac{m{u}^2}{r}=mgm{u}^2=mrgnowusingenergybalance\frac{1}{2}m{u}^2+mg\left(2r\right)=\frac{1}{2}m{v}^2\frac{1}{2}mgr+2mgr=\frac{1}{2}m{v}^2{v}^2=5gracceleration\frac{v^2}{r}=5g=50m/s^2$