Question

A very small particle rests on the top of a hemisphere of radius $20cm$. The smallest horizontal velocity to be given to it, if it is to leave the hemisphere without sliding down its surface taking $g=9.8m/s^2$ is:

• A. $\sqrt{9.8}m/s$
• B. $\sqrt{4.9}m/s$
• C. $\sqrt{1.96}m/s$
• D. $\sqrt{3.92}m/s$

Answer 1

The correct option is C $\sqrt{1.96}m/s$

Critical velocity at the top most point is $\sqrt{g\ell }$
$\therefore$ smallest velocity, such that the particle just leaves the surface =$\sqrt{9.8\times 0.2}=\sqrt{1.96}=1.4m{s}^{-1}$