Question

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

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

Answer 1

Answer: (D)

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