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A small disc is on top of a hemisphere of radius R. What is the smallest horizontal velocity v that should be given to the disc for it to leave the hemisphere and not slide down ? (assume there is no friction)

\[(a)\;v=\sqrt {2gR}\quad (b)\;v=\sqrt {gR} \quad (c)\;v=\sqrt {2R} \quad (d)\;v=\sqrt {g^2 R} \]

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1 Answer

At the top the normal reaction should be zero
When a velocity v is given in the horizontal direction Centripetal force acts
Therefore $mg-N=\large\frac{mv^2}{R}$
When N=0
$v=\sqrt {gR}$
answered Jul 12, 2013 by meena.p

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