Question

A test tube of mass 20 gm is filled with a gas and fitted with a stopper of 2 gm. It is suspended horizontally by means of a thread of 1 m length and heated. When the stopper kicks out, the tube just completes a circle in vertical plane.The velocity with which the stopper is kicked out is

• A. 7 $m{s}^{-1}$
• B. 10 $m{s}^{-1}$
• C. 70 $m{s}^{-1}$
• D. 0.1 $m{s}^{-1}$

Answer 1

Answer: (C)

70 $m{s}^{-1}$

If tubes complete circle

$v^{\prime }=\sqrt{5gR}$

$=\sqrt{5g}$

Conserving momentum

$0=-20\times v^{\prime }+2\times v$

$\Rightarrow v=10\sqrt{5g}$

$v=70$ m/s