Question 519: Centre of Mass and Rotational Motion

Question

Four thin metal rods each of mass ' $M$ ' and length ' $L$ ', are welded end to end to form a square. The moment of inertia of the system about an axis passing through the centre of the square and perpendicular to its plane is

Accepted Answer

Moment of inertia of the system about an axis passing through O
$$\begin{aligned}
\mathrm{I}_0 & =4\left[\mathrm{MI} 	ext { of } \operatorname{rod}+\mathrm{m}\left(\frac{\mathrm{~L}}{2}ight)^2ight] \
& =4\left[\frac{\mathrm{ML}^2}{12}+\frac{\mathrm{ML}^2}{4}ight] \
& =\frac{4}{3} \mathrm{ML}^2
\end{aligned}$$

Answer

$\frac{\mathrm{ML}^2}{3}$

Answer

$\frac{2 \mathrm{ML}^2}{3}$

Answer

$\frac{2 \mathrm{ML}^2}{9}$

Answer

$\frac{4 \mathrm{ML}^2}{3}$

Centre of Mass and Rotational Motion

Four thin metal rods each of mass ' M ' and length ' L ', are welded end to end to form a square. The moment of inertia of the system about an axis passing through the centre of the square and perpendicular to its plane is

Choose the correct answer: