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Q.

A ball of mass m and radius r is rolling without slipping 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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a

2g5(R-r)

b

10 g7(R-r)

c

2g7(R-r)

d

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 = 57mg(R-r)12mv2 = 57mg(R-r)v =10 g(R-r)7ω = vR-r = 10 g7(R-r)
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A ball of mass m and radius r is rolling without slipping 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