Question

A body is just revolved in a vertical circle of radius 'R'. When the body is at highest point, the string breaks. The horizontal distance covered by the body after the string breaks is ______.

पर्याय

• R

• 4R

• 2R

• 3R

Answer 1

A body is just revolved in a vertical circle of radius 'R'. When the body is at highest point, the string breaks. The horizontal distance covered by the body after the string breaks is 2R.

Explanation:

The velocity of the body at the highest point is given by

V = `sqrt"gR"`

After the string breaks, it will fall under gravity with initial horizontal velocity V = `sqrt"gR"`. 

Its initial velocity is vertical direction is zero.

If it falls through a height h, in time t, then

h = `1/2 "gt"^2`

or t = `sqrt("2h"/"g")`

In horizontal direction its velocity will remain constant equal to V.

Distance covered in horizontal direction is x = Vt

`= sqrt("gR") xx sqrt("2h"/"g") = sqrt("2hR")`

IF h = 2R, then x = `sqrt(4"R"^2)` = 2R