If $C$ is the restoring couple per unit radian twist and $I$ is the moment of inertia, the dimension

Question

If $C$ is the restoring couple per unit radian twist and $I$ is the moment of inertia, the dimensional representation of $2 \pi \sqrt{\frac{\mathrm{I}}{\mathrm{C}}}$ will be\

Professor PC Thomas Classes · Answer

I is moment of inertia and C is moment of couple or torque DF of $\mathrm{I}=\mathrm{ML}^{2}$\ DF of $\mathrm{C}=\mathrm{ML}^{2} \mathrm{~T}^{-2}$\ DF of $\sqrt{\frac{\mathrm{I}}{\mathrm{C}}}=\sqrt{\frac{\mathrm{ML}^{2}}{\mathrm{ML}^{2} \mathrm{~T}^{-2}}}=\mathrm{T}$\ $2 \pi$ has no dimension\