Question

A body tied 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

Answer: (B)

$x=2L$

When the string breaks at point P, from there onwards the motion of the body is a projectile motion as if the body is thrown horizontally with velocity $v$ so that AC is the range of the projectile.

For a body to revolve in vertical circle, minimum velocity at the topmost point must be equal to $\sqrt{gL}$

Time of flight $T=\sqrt{\frac{2h}{g}}=\sqrt{\frac{2\left(2L\right)}{g}}=2\sqrt{\frac{L}{g}}$

$\therefore$ Range AC $x=vT=\sqrt{gL}\times 2\sqrt{\frac{L}{g}}=2L$