Question

A small stone of man $0.2\text{kg}$ tied to a massless inextensible string is rotated in a vertical circle of radius of $2\text{m}$. If the particle is just able to complete a vertical circle, what is the speed at the highest point of the circular path? Also, calculate speed if the mass of stone is increased by $50$% (Take $g=10m/s^2)$

• A. $4.47\text{m/s},6.70\text{m/s}$
• B. $4.47\text{m/s},10.05\text{m/s}$
• C. $10.05\text{m/s},4.47\text{m/s}$
• D. $4.47\text{m/s},4.47\text{m/s}$

Answer 1

The correct option is D $4.47\text{m/s},4.47\text{m/s}$

Here $m=0.2\text{kg},r=2\text{m}$
When particle is just able to complete a vertical circle,
$V_{top}=\sqrt{gR}=\sqrt{10\times 2}=4.47\text{m/s}$
As $V_{top}$ does not depends upon mass, it will remain same when mass increases by 50%.