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

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" /> (A) (r/6) (B) (1/4)r (C) (1/3)r (D) (1/2)r

Tardigrade Admin · Accepted Answer

If v velocity acquired at B , then v2=2gh The particle will leave the sphere at B , when ( textmv2/ textr) = textmgcos θ (2 textgh/ textr) = ( textg text. ( textr - texth)/ textr) <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-zqh54wyktrzy.png" /> Which gives h=(r/3)

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

$\frac{r}{6}$

$\frac{1}{4} r$

$\frac{1}{3} r$

$\frac{1}{2} r$

If $v$ velocity acquired at $B$ , then
$v^{2} = 2 g h$
The particle will leave the sphere at $B$ , when
$\frac{mv ^{2}}{r} = mgcos θ$
$\frac{2 gh}{r} = \frac{g . ( r - h )}{r}$

Which gives $h = \frac{r}{3}$

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

6r​

41​r

31​r

21​r