Question

A sphere of mass $2000g$ and radius $5cm$ is rotating at the rate of $300rpm$. Then the torque required to stop it in $2\pi$ revolutions, is

• A. $1.6\times {10}^{2}dynecm$
• B. $1.6\times {10}^{3}dynecm$
• C. $2.5\times {10}^{4}dynecm$
• D. $2.5\times {10}^{5}dynecm$

Answer 1

Answer: (D)

$2.5\times {10}^{5}dynecm$

Use $\tau =I\alpha$
and ${\omega }^2-{\omega }_0^2=2\alpha \theta$
Here $I=\frac{2}{5}M{R}^2$
Given $M=2000g=2kg$
$R=5cm=5\times {10}^{-2}m$
$\theta =2\pi \times 2\pi$ radians
$n=300rpm=5rps$
$\therefore \tau =I\alpha =\left(\frac{2}{5}M{R}^2\right)\left(\frac{{\omega }^2-{\omega }_0^2}{2\theta }\right)$
$=\frac{2}{5}\times 2\times {(5\times {10}^{-2})}^2\frac{4{\pi }^2(5^2-0^2)}{2\times 4{\pi }^2}$
$=0.025N-m$
$=2.5\times {10}^{5}dynecm$