Question

A stone of mass $5\text{kg}$ is tied to a string of length $2.5\text{m}$, is whirled round in a horizontal circle. What is the maximum angular velocity with which the stone can be whirled around, if the string can withstand a maximum tension of $1250\text{N}$ ?

• A. $30\text{rad/s}$
• B. $20\text{rad/s}$
• C. $10\text{rad/s}$
• D. $5\text{rad/s}$

Answer 1

The correct option is C $10\text{rad/s}$

It is given that the breaking tension of string $\left(T_{\text{max}}\right)=1250\text{N}$.

To find maximum angular velocity ${\omega }_{\text{max}}:$
$T_{\text{max}}=ml{\omega }_{\text{max}}^2$
where $\left(l\right)$ is length of the string.

${\omega }_{\text{max}}^2=\frac{T_{\text{max}}}{ml}$
$\Rightarrow {\omega }_{\text{max}}=\sqrt{\frac{T_{\text{max}}}{ml}}=\sqrt{\frac{1250}{5\times \frac{5}{2}}}=\sqrt{\frac{2500}{25}}=\sqrt{100}=10\text{rad/s}$