Question

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

पर्याय

• mL²

• 3mL²

• 2mL²

• `sqrt3`mL²

Answer 1

Four point masses, each of value m, are placed at the comers of a square ABCD of side L, the moment of inertia of this system about an axis through A and parallel to BD is 3mL².

Explanation:

Moment of inertia of the system about given axis

I = I₁ + I₂ + I₃ + I₄

r₂ = r₄ = OA = `l/sqrt2, "r"_3 = lsqrt2`

I = O + m(r₂)² + m(r₃)² + m(r₄)²

`= "I" = "m"(1/sqrt2)^2 + "m"(lsqrt2)^2 + "m"(1/sqrt2)^2`

∴ I = 3 ml²