Question

A body is tied up by 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:

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

Answer 1

The correct option is B $x=2l$

$\frac{m{v}^2}{l}=mgv=\sqrt{lg}h=2l$

Time to fall height h under geavity =t

$\therefore \frac{1}{2}g{t}^2=ht=\sqrt{\frac{2h}{h}}$

Horizontal range is

$=vt=\sqrt{lg}\times \sqrt{\frac{2h}{g}}=\sqrt{2hl}=\sqrt{2\times 2l\times l}=2l$