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 ______.

Options

• ml²

• 3 ml²

• `sqrt3  "ml"^2`

• 2 ml²

Answer 1

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 3 ml².

Explanation:

In ΔABC, ∠B = 90°

AC² = AB² + BC² 

AC² = l² + l²

AC = `sqrt(2"l"^2)` ⇒ `sqrt2"l"` 

Length of the diagonal of a square

d = BE = AO = `"AC"/2="l"/sqrt2`

Moment of Inertia about the axis passing through A.

I = m(0)² + m(d)² + m(d)² + m(AC)²

I = 2md² + m(AC)² = 2m `["l"/sqrt2]^2 + "m" [sqrt2"l"]^2`

⇒ `2"m""l"^2/2+2"ml"^2`

⇒ 3ml²