Question

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

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

Answer 1

The correct option is B $4{\text{rad s}}^{-1}$

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

The force equation at the bottom most point
$T-mg=m{\omega }^{2}r$
$\Rightarrow m{\omega }^{2}r=T-5$
For maximum angular speed, the tension must be maximum i.e. $37\text{N}$
Mass of the stone is $500\text{g}=\frac{1}{2}\text{kg}$

$\Rightarrow {\omega }^2=\frac{32\times 2}{1\times r}=\frac{64}{4}$

$\omega =4\text{rad/s}$

Hence option B is the correct answer