The moment of inertia of a thin rod about an axis passing through its mid point and perpendicular to

Question

The moment of inertia of a thin rod about an axis passing through its mid point and perpendicular to the rod is $2400 \mathrm{~g} \mathrm{~cm}^2$. The length of the 400 g rod is nearly

Professor PC Thomas Classes · Answer

(a) : Moment of inertia of $a$ thin rod about an axis passing through its mid point and perpendicular to the rod $ I_{\mathrm{cm}}=\frac{M l^2}{12} $ \ where, $M=$ Mass of the rod, $l=$ Length of the rod Given, \ $M=400 \mathrm{~g}, l=$ ?, $I_{\mathrm{cm}}=2400 \mathrm{~g} \mathrm{~cm}^2$ \ From eq (i), $l=\sqrt{\frac{I_{\mathrm{cm}} 	imes 12}{M}}=\sqrt{\frac{2400 	imes 12}{400}}=8.484 \approx 8.5 \mathrm{~cm}$