Question

A body of mass $5kg$ acquires an acceleration of $10rad.s^{-2}$ due to an applied torque of $2Nm$. Its radius of gyration is__________

• A. $2.5m$
• B. $\sqrt{2.5}m$
• C. $\sqrt{0.2}m$
• D. $0.2m$

Answer 1

Answer: (D)

Mass of body, $m=5kg$
Angular acceleration, $\alpha =10rad{s}^{-2}$
Torque, $\tau =2N-m$
We know that,
Torque $=$ Moment of inertia $\times$ Angular acceleration
$\Rightarrow \tau =I\alpha$
$\Rightarrow I=\frac{\tau }{\alpha }=\frac{2}{10}$
$I=0.2kg-m^2$
If $k$ be the radius of gyration,
then $I=m{k}^2$
$\Rightarrow k=\sqrt{\frac{I}{m}}=\sqrt{\frac{0.2}{5}}$
$=\sqrt{0.04}=0.2m$