First slide

Force

Question

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

Easy

A

$\sqrt{g R}$
B

$\sqrt{2 g R}$
C

$\sqrt{3 g R}$
D

$\sqrt{5 g R}$

Solution

The velocity should be such that the centripetal acceleration is equal to the acceleration due to gravity
$\frac{V^{2}}{R} = g or V = \sqrt{gR}$

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