A body is tied up a string of length l and rotated in vertical circle at minimum speed. When it reaches at highest point string breaks and body moves on a parabolic path in presence of gravity according to fig. in the plane of point A, value of horizontal range AC will be

Options

A. `x=L`
B. `x=2L`
C. `x=2sqrt(2)L`
D. `x=sqrt(2)L`

Answer

B

Explanation

For looping the loop minimum velocity at top
point `v=sqrt(gL)`
time taken by particle
`t=sqrt((2h)/(g))=sqrt((2xx2L)/(g)) = 2sqrt((L)/(g))`
`therefore ` horizontal range `x=vt=sqrt(gL) xx 2 sqrt((L)/(g))=2L`