A body is just being revolved in a vertical circle of radius R. The string breaks when the body is at the highest point . What is the horizontal distance covered by the body after the string breaks ?

Options

A. `R `
B. `R sqrt(2)`
C. `4R `
D. `2R`

Answer

D

Explanation

when the body is at the highest point , it is at a distance `h= 2R ` from the ground . Its velocity at the highest point `=sqrt(g R)`
when the string breaks , the body acts like a projectile at its highest point , with its horizontal velocity `= sqrt( g R)` . The time taken by it to reach the ground is given by
`h=(1)/(2) g t ^2 " " therefore t = sqrt((2h)/(g) ) = sqrt((2xx2R)/(g ))=2sqrt((R )/(g))`
`therefore ` The horizontal distance travelled by the body
= horizontal velocity `xx` time
`= sqrt(g R) xx2sqrt((R )/(g ))=2 sqrt((R )/(g )xxg R )=2R `