Question

A body of mass $10kg$ is attached to a wire $0.3m$ long. Its breaking stress is 4.8 x 10${}^7$ N/m${}^2$. The area of cross section of the wire is ${10}^{-6}{m}^2$. The maximum angular velocity with which it can be rotated in a horizontal circle without breaking is :

• A. $2rad/s$
• B. $4rad/s$
• C. $6rad/s$
• D. $8rad/s$

Answer 1

The correct option is B $4rad/s$

$stress=\frac{force}{Area}$

$Force=stress\times Area$

$=4.8\times {10}^7\times {10}^{-}6$

$=48$

Now, $\text{Force=Tension in wire}=m{\omega }^{2}r$

So, $48=m{\omega }^{2}r$

$\Rightarrow \frac{48}{0.3}\times \frac{1}{10}={\omega }^2$

$\Rightarrow \omega =4rad/s$