Question

A string of length $0.1m$ cannot bear a tension more than $100N$. It is tied to a body of mass $100g$ and rotated in a horizontal circle. The maximum angular velocity can be :

• A. $100rad/s$
• B. $1000rad/s$
• C. $10000rad/s$
• D. $0.1rad/s$

Answer 1

The correct option is A $100rad/s$

Given,

$r=0.1m$

$T=100N$

$m=100g=0.1kg$

Tension $T$ provide both tangential force and centripetal force.

$T=\frac{m{v}^2}{r}$

$T=m{\omega }^{2}r$

$100=0.1\times 0.1{\omega }^2$

${\omega }^2=10000$

$\omega =\sqrt{10000}$

$\omega =100rad/s$

The correct option is A.