Question

A ball of mass $500\text{gm}$ is tied to one end of a rope of length $3\text{m}$. The other end is fixed and the ball is now moving along a horizontal circle with uniform angular speed of $2\text{rev/s}$. The tension in the rope (in $\text{newton}$) will be:

• A. $304{\pi }^2$
• B. $6{\pi }^2$
• C. $24{\pi }^2$
• D. $24000{\pi }^2$

Answer 1

The correct option is C $24{\pi }^2$


Since tension in rope is acting towards centre, it is the source of centripetal force for the body.
Applying equation of cirular motion along radial direction,
$T=mr{\omega }^2$
Given $\omega =2\text{rev/s}=2\times 2\pi \text{rad/s}$
$m=0.5\text{kg},r=3\text{m}$
$\Rightarrow T=0.5\times 3\times (4\pi {)}^2=24{\pi }^2\text{N}$