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 ?

Step-by-step solution

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.