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)

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m g cos θ = m v 2 R . . . ( 1 ) cos θ = h R Energy conservation m g { R - h } = 1 2 m v 2 . . . ( 2 ) from ( 1 ) and ( 2 ) ⇒ m g h R = 2 m g { R - h } R h = 2 R 3 = 2 m

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