Question

Dry gas of negligible mass is sealed in a test tube of mass $50gm$ with the help of a stopper of mass $3.5gm$. The test tube is suspended form a fixed point with help of massless string such that the test tube is horizontal and distance between point of suspension and centre of mass of test tube is $25cm$. The test tube is heated to a temperature due to which stopper is ejected out horizontally while test tube completes a vertical circle of radius $25cm$. The minimum velocity with which stopper should be ejected out is:

• A. $72kmph$
• B. $90kmph$
• C. $180kmph$
• D. $360kmph$

Answer 1

Answer: (C)

$180kmph$

for completing a complete circle , mean velocity given should be $\sqrt{5gr.}$
$v_1=\sqrt{5\times 10\times \frac{1}{4}}=\sqrt{\frac{25}{2}}mVs.$
Conservation of linear momentum
$m_1{v}_1=m_2{v}_2$
$\left(50\right)\sqrt{\frac{25}{2}}=\left(3.5\right)\left(Vs\right)$
$50.5mvs.=Vs$
$vs=181.8kmphr.$