Question 527: Centre of Mass and Rotational Motion

Question

Three thin rods, each mass ' 2 M ' and length ' L ' are placed along $\mathrm{x}, \mathrm{y}$ and z axis which are mutually perpendicular. One end of each rod is at origin. Moment of inertia of the system about x - axis is

Accepted Answer

$$\begin{aligned}
&	ext { Total moment of inertia, }\
&\mathrm{I}_{	ext {total }}=\mathrm{I}_{\mathrm{x}}+\mathrm{I}_{\mathrm{y}}+\mathrm{I}_{\mathrm{z}}\quad	ext{.... (i)}
\end{aligned}$$
Moment of inertia of thin rod, when axis is passing through one end and perpendicular to the rod,
$$\begin{aligned}
& \mathrm{I}=\frac{\mathrm{ML}^2}{3} \quad	ext{.... (ii)}\
& \mathrm{I}_{\mathrm{y}}=\frac{\mathrm{M}_{\mathrm{y}} \mathrm{~L}^2}{3}=\frac{2 \mathrm{ML}^2}{3}\quad	ext{.... [From (i)]}
\end{aligned}$$
$\ldots$ (given, $\left.\mathrm{M}_{\mathrm{y}}=2 \mathrm{M}ight)$
Similarly,
$$\mathrm{I}_2=\frac{\mathrm{M}_{\mathrm{z}} \mathrm{~L}^2}{3}=\frac{2 \mathrm{ML}^2}{3}\quad	ext{.... [From (ii)]}$$
$\ldots\left(ight.$ given, $\mathrm{M}_{\mathrm{z}}=2 \mathrm{M}$)
$$\begin{aligned}
& \mathrm{I}_{\mathrm{x}}=0 \quad \ldots(\because 	ext { Rod lies along } \mathrm{X} 	ext {-axis }) \
& 	ext { Substituting in (i), } \
	herefore \quad & \mathrm{I}_{	ext {total }}=\frac{4 \mathrm{ML}^2}{3}
\end{aligned}$$

Answer

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

Answer

$\frac{\mathrm{ML}^2}{12}$

Answer

$\frac{\mathrm{ML}^2}{6}$

Answer

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

Centre of Mass and Rotational Motion

Three thin rods, each mass ' 2 M ' and length ' L ' are placed along \mathrm{x}, \mathrm{y} and z axis which are mutually perpendicular. One end of each rod is at origin. Moment of inertia of the system about x - axis is

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