Q. A particle rests on the top of a hemisphere of radius $R$. Find the smallest horizontal velocity that must be imparted to the particle if it is to leave the hemisphere without sliding down it
A) $\sqrt{g\ R}$
B) $\sqrt{2g\ R}$
C) $\sqrt{3g\ R}$
D) $\sqrt{5g\ R}$
Explanation
(a) The velocity should be such that the centripetal acceleration is equal to the acceleration due to gravity $ie,v^{2}/R = g$ or $v = \sqrt{gR}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.