Three thin rods, each of mass ' $M$ ' and length ' $L$ ' are placed along $X, Y$ and Z axes which are…

Three thin rods, each of mass ' $M$ ' and length ' $L$ ' are placed along $X, Y$ and Z axes which are mutually perpendicular. One end of each rod is at origin. M. I. of the system about Z axis is
  1. $\frac{3 \mathrm{ML}^2}{4}$
  2. $\frac{2 \mathrm{ML}^2}{5}$
  3. $\frac{2 \mathrm{ML}^2}{3}$
  4. $\frac{3 \mathrm{ML}^2}{5}$

Solution

$\begin{array}{ll} & I=\mathrm{I}_1+\mathrm{I}_2+\mathrm{I}_3 \\ \therefore \quad & \mathrm{I}=\frac{\mathrm{ML}^2}{3}+\frac{\mathrm{ML}^2}{3}+0 \\ \therefore \quad & \mathrm{I}=\frac{2 \mathrm{ML}^2}{3}\end{array}$
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Asked in: MHT CET 2024 (15 May Shift 1)

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