Question

A weightless thread can bear tension upto $37N$. A stone of mass $500g$ is tied to it and revolved in a circular path of radius $4m$ in a vertical plane. If $g=10{ms}^{-2}$, then the maximum angular velocity of the stone will be:

• A. $2rad{s}^{-1}$
• B. $4rad{s}^{-1}$
• C. $8rad{s}^{-1}$
• D. $16rad{s}^{-1}$

Answer 1

Answer: (B)

$4rad{s}^{-1}$

Maximum tension in the string will be at the lowest point of the circular path, where the tension will support the weight as well as provide the centripetal force for circular motion.

So, we have:

$T=mg+ml{\omega }^2$

$\Rightarrow ml{\omega }^2=T-5$

For maximum angular speed, the tension must be $37N$

So, the maximum angular speed is $\sqrt{\frac{T-5}{ml}}=\sqrt{\frac{37-5}{0.5\times 4}}=4rad/s$

Thus, ${\omega }_{max}=4rad/s$