question_answer

            Four point masses, each of value m, are placed at the comers of a square ABCD of side \[\ell \].The moment of inertia of this system about an axis passing through A and parallel to BD is

A) \[2m{{\ell }^{2}}\]

B) \[\sqrt{3}m{{\ell }^{2}}\]

C) \[3m{{\ell }^{2}}\]

D) \[m{{\ell }^{2}}\]

Correct Answer: C

Solution :

[c] \[{{I}_{nn'}}=M.I\]due to the point mass at \[B+M.I\]due to the point mass at \[D+M.I\]due to the point mass at C. \[=2\times m{{\left( \frac{\ell }{\sqrt{2}} \right)}^{2}}+m{{(\sqrt{2}\ell )}^{2}}=m{{\ell }^{2}}+2m{{\ell }^{2}}=3m{{\ell }^{2}}\]