Question

A small body of mass m is placed on the top of a hemisphere of radius r.
Then the smallest horizontal velocity that should be given to the body so
that it may leave the hemispherical surface and not slide down is
(A) Vgr
(B) 2gr
(C) 3gr
(D) 2gr​

Answer 1

Answer:

The answer is 2gr

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Answer 2

Answer: $\sqrt{gr}$

Explanation:

$mg - N = \frac{mv^{2} }{r}$

Since it leaves the surface $N = 0$

$mg = \frac{mv^{2} }{r}$

$g = \frac{v^{2} }{r}$

$rg =v^{2}$

Hence,

$v = \sqrt{gr}$