Question

A body ties to a string of length $L$ is revolved in a vertical circle with minimum velocity, when the body reaches the upper most point the string breaks and the body moves under the influence of the gravitational field of earth along a parabolic path. The horizontal range $AC$ of the body will be:

• A. $x=L$
• B. $x=2L$
• C. $x=2\sqrt{2L}$
• D. $x=\sqrt{2L}$

Answer 1

The correct option is B $x=2L$

Time taken to reach the body ground $ut$

$2L=\frac{1}{2}g{t}^{2}t=\sqrt{\frac{4L}{g}}$

Now

$x=vt⟶1$

Now if body move in vertical circle withminimum speed then at top point P.

$\frac{v^2}{L}=gV=\sqrt{Lg}$

Now equation $1$ becomes

$x=\sqrt{Lg}\times \sqrt{\frac{4L}{g}}=2L$