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, such that h is equal to ______.

Options

• `1/6`r

• `1/4`r

• `1/3`r

• `1/2`r

Answer 1

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, such that h is equal to `underlinebb(1/3"r")`.

Explanation:

If v velocity acquired at B, then

v² = 2gh

The particle will leave the sphere at B, when

`"mv"^2/"r"` = mgcosθ

`(2"gh")/"r"=("g".("r"-"h"))/"r"`

Which gives h = `"r"/3`