Four point masses, each of value m, are placed at the corners of a square ABCD of side 1. The moment of inertia of this system about an axis through A and parallel to BD is

Options

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

Answer

D

Explanation

`AO = cos 45^(@) = (l)/(2)`
`therefore AO xx (1)/(sqrt2) = (l)/(2)`
or `AO = (l)/(sqrt2)`
`I = I_(D) + I_(B) + I_(C)`
or `I = (2ml^2)/(2) + m ((2l)/(sqrt2))^(2)`
= `(2ml^(2))/(2) + (4ml^2)/(2)`
or `I = (6ml^2)/(2) = 3ml^2`