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3-2.Motion in Plane
hard
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 $R$ ?
A
B
C
D
(JEE MAIN-2022)
Solution
$V =\sqrt{2 gR \sin \alpha}$$N-m g \sin \alpha=\frac{m v^{2}}{R}=2 m g \sin \alpha$
$\frac{N}{2 m g \sin \alpha}=\frac{1}{2}+1=\frac{3}{2}$
$\Rightarrow A =\text { constant }$
Standard 11
Physics
