Question 254 of 308

A small block slides down from the top of hemisphere of radius $R=3m$ as shown in the figure. The height $h$ at which the block will lose contact with the surface of the sphere is $m$. (Assume there is no friction between the block and the hemisphere)

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Answer: 2

$mg\cos \theta =\dfrac{m{v}^{2}}{R}...(1)$
$\cos \theta =\dfrac{h}{R}$
Energy conservation
$mg{R-h}=\dfrac{1}{2}m{v}^{2}$ $...(2)$
from $(1)$ and $(2)\Rightarrow mg\left\{\dfrac{h}{R}\right\}=\dfrac{2mg{R-h}}{R}$
$h=\dfrac{2R}{3}=2m$