Question

A stone of mass $2\text{kg}$ is tied to one end of a rope of length $2\text{m}$. The other end is fixed to a vertical axis, around which the mass is performing a circular motion with an angular speed of $2\pi \text{rad/s}$. Then, tension in the rope (in $\text{newtons}$) will be:

• A. $16{\pi }^2$
• B. $8{\pi }^2$
• C. $4{\pi }^2$
• D. $6{\pi }^2$

Answer 1

The correct option is A $16{\pi }^2$


Tension in the rope is the only source of required centripetal force for the stone.
Angular speed of stone for circular path is $\omega =2\pi \text{rad/s}$
and mass of stone $m=2\text{kg}$

Applying equation of circular dynamics along radial direction gives:

$T=mr{w}^2$
$=2\times 2\times (2\pi {)}^2$
$=4\times (2\pi {)}^2=16{\pi }^2\text{N}$