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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?

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answer is C.

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Detailed Solution

$V = \sqrt{2 g R \sin α}$

$N - m a \sin α = \frac{m v^{2}}{R} = 2 m g \sin α$

$\frac{N}{2 m g \sin α} = \frac{1}{2} + 1 = \frac{3}{2}$

$\Rightarrow A =$ constant

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