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  4. In figure, a particle is placed at the highest point A of a smooth sphere of radius r . It is given slight push, and it leaves the sphere at B , at a depth h vertically below A . The value of h is <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-zqh54wykpvuh.png />

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Q. In figure, a particle is placed at the highest point $A$ of a smooth sphere of radius $r$ . It is given slight push, and it leaves the sphere at $B$ , at a depth $h \, $ vertically below $A$ . The value of $h$ is

Question

NTA AbhyasNTA Abhyas 2020Laws of Motion

Solution:

If $v$ velocity acquired at $B$ , then
$v^{2}=2gh$
The particle will leave the sphere at $B$ , when
$\frac{\text{mv}^{2}}{\text{r}} = \text{mgcos} \theta $
$\frac{2 \text{gh}}{\text{r}} = \frac{\text{g} \text{.} \left(\text{r} - \text{h}\right)}{\text{r}}$
Solution
Which gives $h=\frac{r}{3}$