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Four equal masses, m each are placed at the corners of a square of length (l) as shown in the figure.

Question:

Four equal masses, m each are placed at the corners of a square of length (l) as shown in the figure. The moment of inertia of the system about an axis passing through A and parallel to DB would be : 

  1. $\mathrm{m} l^{2}$

  2. $2 \mathrm{~m} l^{2}$

  3. $3 \mathrm{~m} l^{2}$

  4. $\sqrt{3} \mathrm{ml} l^{2}$

Correct Option: , 3

Solution:

Moment of inertia of point mass

$=$ mass $\times(\text { Perpendicular distance from axis })^{2}$

Moment of Inertia

$=\mathrm{m}(0)^{2}+\mathrm{m}(l \sqrt{2})^{2}+\mathrm{m}\left(\frac{l}{\sqrt{2}}\right)^{2}+\mathrm{m}\left(\frac{l}{\sqrt{2}}\right)^{2}$

$=3 \mathrm{~m} l^{2}$

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