Four thin metal rods each of mass ' $M$ ' and length ' $L$ ', are welded end to end to form a square. The…

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
  1. $\frac{\mathrm{ML}^2}{3}$
  2. $\frac{2 \mathrm{ML}^2}{3}$
  3. $\frac{2 \mathrm{ML}^2}{9}$
  4. $\frac{4 \mathrm{ML}^2}{3}$

Solution


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

Asked in: MHT CET 2024 (11 May Shift 2)

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