Question

A body is rotated in the vertical plane by means of a thread of length $l$ with minimum possible velocity. When the body goes up and reaches at the highest point B of its path, the thread breaks and the body moves on a parabolic path under the influence the gravitational field as shown in the diagram. The horizontal range AC would be

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

Answer 1

The correct option is B $x=2l$


From energy conservation.
for complete verticle circle
$u_{min}=\sqrt{5gl}$
$\frac{1}{2}m{v}_A^2=\frac{1}{2}m{v}_B^2+2mgl$
$\frac{1}{2}m5gl=\frac{1}{2}\times m{v}_B^2+2mgl$
$\frac{mgl}{2}=\frac{1}{2}m{v}_B^2$
$V_B=\sqrt{gl}$
from equation of motion.
$2l=0+\frac{1}{2}g{t}^2$
$t=\sqrt{\frac{4l}{g}}$
Range $\left(AC\right)=V_B\times t=\sqrt{gl}\times \sqrt{\frac{4l}{g}}$
Range $R=2l$