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 positio

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 $R$ ?

TestHub · Accepted Answer

At angular position α as shown in the figure, applying conservation of mechanical energy m g R sin α = 1 2 m v 2 ⇒ m v 2 R = 2 m g sin α In the radial direction, N - m g sin α = m v 2 R ⇒ N = 3 m g sin α Now the ratio of centripetal force and normal reaction is, A = m v 2 R N = 2 m g sin α 3 m g sin α = 2 3 . Therefore, A is constant.

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