A small block slides down from top of hemisphere of radius R=3, {m} as shown in figure. height '

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5.Work, Energy, Power and Collision

hard

A small block slides down from the top of hemisphere of radius $R=3\, {m}$ 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)

A

$1$

B

$2$

C

$3$

D

$4$

(JEE MAIN-2021)

Solution

on balancing

$m g \cos \theta=\frac{m v^{2}}{R}….(1)$

$\cos \theta=\frac{h}{R}$

Energy conservation

$m g\{R-h\}=\frac{1}{2} m v^{2}….(2)$

From $(1)$ and $(2) \Rightarrow m g\left\{\frac{h}{R}\right\}=\frac{2 m g\{R-h\}}{R}$

$h=\frac{2 R}{3}=2\, m$

Standard 11

Physics

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