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  4. 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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Q. 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 $\alpha$ with respect to point $P$. Which of the following graphs represent the correct relation between $A$ and $\alpha$ when ball goes from $Q$ to $R$ ?Physics Question Image

JEE MainJEE Main 2022Laws of Motion

Solution:

$V=\sqrt{2 g R \sin \alpha}$
$N-m g \sin \alpha=\frac{m v^{2}}{R}=2 m g \sin \alpha$
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$\frac{ N }{2 mg \sin \alpha}=\frac{1}{2}+1=\frac{3}{2}$
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$\Rightarrow A =$ constant