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  4. A sphere of mass m makes SHM in a hemispherical bowl ABC . It moves from A to C , and then back to A via ABC . It is considered that PB=h . If acceleration due to gravity be g then the speed of the ball when it just crosses the point B will be, <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-k2lpo11xnr4rdakn.jpg />

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Q. A sphere of mass $m$ makes SHM in a hemispherical bowl $ABC$ . It moves from $A$ to $C$ , and then back to $A$ via $ABC$ . It is considered that $PB=h$ . If acceleration due to gravity be $g$ then the speed of the ball when it just crosses the point $B$ will be,
Question

NTA AbhyasNTA Abhyas 2020

Solution:

Potential energy at $A$ is converted into K.E. at $B$
$\therefore mgh=\frac{1}{2}mv_{B}^{2}=2gh,v_{B}=\sqrt{2 g h}$