System Of Particles And Rotational Motion Ques 64

64. Four identical thin rods each of mass $M$ and length $l$, form a square frame. Moment of inertia of this frame about an axis through the centre of the square and perpendicular to its plane is :

[2009]

(a) $\frac{2}{3} $ $Ml^{2}$

(b) $\frac{13}{3} $ $Ml^{2}$

(c) $\frac{1}{3} $ $Ml^{2}$

(d) $\frac{4}{3} $ $Ml^{2}$

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Answer:

Correct Answer: 64.(d)

Solution:

  1. (d) Moment of inertia of a thin rod of length $l$ about an axis passing through centre and perpendicular to the $rod=\frac{1}{12}ML^{2}$.

The moment of inertia of the frame.

$\frac{ml^{2}}{12}+\frac{ml^{2}}{4}=\frac{4 ml^{2}}{12}=\frac{ml^{2}}{3}$

Total M.I. $=4 \times \frac{m l^{2}}{3}$

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