Question

A body of mass $5 \,kg$ acquires an angular acceleration of $10\, rad\, s^{-2}$ by an applied torque of $2 \,N m$ . Find its radius of gyration.

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

Answer 1

Answer: (D)

$0.2\,m$

Answer 2

$m=5\,Kg$,
$\alpha=10$ rad $s^{-2}$,
$\tau=2\,N\,m$
Torque, $\tau=I \alpha=mk^{2}\alpha \left(\because I=mk^{2}\right)$
where $k$ is the radius of gyration
$\therefore 2=5\times k^{2}\times10$
or $k^{2}=0.04$ or $k=0.2\,m$