Chapter 7 - Circular Motion and Gravitation - Learning Path Questions and Exercises - Exercises - Page 262: 41

a). Minimum $v=\sqrt (gr)$. b). $h=\frac{5}{2}r$.

a). Centripetal force = weight of the body $\frac{mv^{2}}{r}=mg$ Thus, minimum $v=\sqrt (gr)$. b). Thus, by conservation of energy, $mgh=\frac{1}{2}mv^{2}+mg(2r)=\frac{1}{2}mgr+2mgr=\frac{5}{2}mgr$ $h=\frac{5}{2}r$.