A body of mass 1.5 kg rotating about an axis with angular velocity of $0.3 \mathrm{rads}^{-1}$ has t

Question

A body of mass 1.5 kg rotating about an axis with angular velocity of $0.3 \mathrm{rads}^{-1}$ has the angular momentum of $1.8 \mathrm{kgm}^{2}$. The radius gyration of the body about an axis is\

Professor PC Thomas Classes · Answer

Here $\mathrm{L}=1.8 \mathrm{~kg} \mathrm{~m}^{2} \mathrm{~s}^{-1}, \mathrm{M}=1.5 \mathrm{~kg}$\ $\omega=0.3 \mathrm{rad} \mathrm{s}^{-1}$\ Radius of gyration $\mathrm{k}=\frac{\sqrt{\mathrm{I}}}{\mathrm{M}}$\ $\mathrm{I}=\mathrm{Mk}^{2}$ Angular momentum, $\mathrm{L}=\mathrm{I} \omega$\ $\mathrm{L}=\mathrm{k}^{2} \mathrm{M} \omega$\ (using (i) and (ii)\ or $1.8=\mathrm{k}^{2} 	imes 1.5 	imes(0.3)$\ $\Rightarrow \mathrm{k}^{2}=\frac{1.8}{1.5 	imes 0.3}=4$\ $\Rightarrow \mathrm{k}=2 \mathrm{~m}$\