A ball is released from rest from point P of a smooth semi-spherical vessel as shown in figure. The ratio of the centripetal force and normal reaction…

Question

A ball is released from rest from point $P$ of a smooth semi-spherical vessel as shown in figure. The ratio of the centripetal force and normal reaction on the ball at point $Q$ is $A$ while angular position of point $Q$ is $α$ with respect to point $P$ . Which of the following graphs represent the correct relation between $A$ and $α$ when ball goes from $Q$ to $R$ ?

MARKS Content Team · Accepted Answer

Correct answer: (C). At angular position α as shown in the figure, applying conservation of mechanical energy mgRsinα=1/2mv^2⇒(mv^2)/R=2mgsinα In the radial direction, N-mgsinα=(mv^2)/R⇒N=3mgsinα Now the ratio of centripetal force and normal reaction is, A=(mv^2R)/N=(2mgsinα)/(3mgsinα)=2/3. Therefore, A is constant.

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