Question

A body of mass $1\text{kg}$ is tied to one end of a string $2\text{m}$ long. The other end is fixed and the body revolves in a horizontal circle. The maximum tension the string can bear is $80\text{kg wt}$. The maximum frequency the body can have (in $rev/s$) is (Take $g=10{\text{m/s}}^2$)

• A. $20$
• B. $\frac{\pi }{10}$
• C. $\frac{10}{\pi }$
• D. None

Answer 1

The correct option is C $\frac{10}{\pi }$

Given, mass of body $\left(m\right)=1\text{kg}$
Length of string $\left(l\right)=2\text{m}$
Maximum tension in string $\left(T_{\text{max}}\right)=80\text{kg wt}=80\times 10=800\text{N}$

Since, tension provides necessary centripetal force.

$T_{\text{max}}=ml{\omega }_{\text{max}}^2$
${\omega }_{\text{max}}^2=\frac{T_{\text{max}}}{ml}$
${\omega }_{\text{max}}=\sqrt{\frac{T_{\text{max}}}{ml}}=\sqrt{\frac{800}{2}}=20$

Hence, the maximum frequency will be, (as $\omega =2\pi f$)

$f_{\text{max}}=\frac{20}{2\pi }=\frac{10}{\pi }\text{rev/sec}$

Hence option C is the correct answer