Question

A stone of mass $2kg$ is fastened to one end of a steel wire of cross sectional area $2m{m}^2$ and is whirled in a horizontal circle of radius $25cm$. If the breaking stress of steel is $1.2\times {10}^{9}N{m}^{-2}$ find the maximum number of revolutions the stone can make per minute without the string breaking.

• A. $661.5rpm$
• B. $331.5rpm$
• C. $221.5rpm$
• D. $441.5rpm$

Answer 1

The correct option is A $661.5rpm$

Given,

Mass of stone, $m=2kg$

Steel wire of cross-sectional area, $A=2m{m}^2=2\times {10}^{-6}{m}^2$

Breaking stress of steel is $Y=1.2\times {10}^{9}N{m}^{-2}$

Whirled in a horizontal circle of radius, $r=25cm=0.25m$.

Tension in cable due to rotation,$T=mr{\omega }^2$

$Y=\frac{T}{A}=\frac{mr{\omega }^2}{A}$

$\Rightarrow \omega =\sqrt{\frac{YA}{mr}}=\sqrt{\frac{1.2\times {10}^9\times 2\times {10}^{-6}}{2\times 0.25}}=69.28rad/s$

$\omega =\frac{2\pi f}{60}$

$f=\frac{60\omega }{2\pi }=\frac{60\times 69.28}{2\pi }=661.57rev/min$

The maximum number of revolutions the stone can make per minute without the string breaking is $661.57rev/min$