A ball of mass m and radius r rolls inside a hemispherical shell of radius R. It is released from rest from point A as shown in figure. The angular velocity of centre of the ball in position B about the centre of the shell is

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2 g5(R-r)

2 R7(R-r)

2g7(R-r)

5g2(R-r)

answer is B.

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Detailed Solution

K.E. of ball in position B = mg(R - r)Here m = mass of ball.Since it rolls without slipping the ratio of rotational to translational kinetic energy will be 25.KRKT = 25KT = 27mg(R-r)12mv2 = 27mg(R-r)v = 27g(R-r)ω = vR-r = 2g7(R-r)

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