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

Options

A. `2ml^(2)`
B. `sqrt3 ml^(2)`
C. `3ml^(2)`
D. `ml^(2)`

Answer

C

Explanation

The situation is shown in the figure.
`l_("XX'")=mxxDP^(2)+mxx BQ^(2)+mxxCA^(2)`
`AC=lsqrt2`
`PD=QB=(AC)/(2)=(l)/(sqrt2)`

`=mxx2xx((sqrt2l)/(2))^(2)+m xx(sqrt2l)^(2)=3ml^(2)`