Question

A stone of mass of $16\text{kg}$ is attached to a string $144\text{m}$ long and is whirled in a horizontal smooth surface. The maximum tension the string can withstand is $16\text{N}$. The maximum speed of revolution of the stone without breaking it will be (in ${\text{ms}}^{-1}$)

Answer 1

Given

For circular motion
Tension in the string = Centrifugal force
$T=\frac{m{v}^2}{R}$
$v^2=\frac{RT}{m}$
Given that
$T_{max}=16\text{N}$
$v_{max}=\sqrt{\frac{RT}{m}}$
$\Rightarrow v_{max}=\sqrt{\frac{16\times 144}{16}}=12\text{m/s}$