Question

Moment of inertia (M.I.) of four bodies, having same mass and radius, are reported as :

I₁ = M.I. of thin circular ring about its diameter,

I₂ = M.I. of circular disc about an axis perpendicular to disc and going through the centre,

I₃ = M.I. of solid cylinder about its axis and

I₄ = M.I. of solid sphere about its diameter.

Then -

Options

• I₁ = I₂ = I₃ < I₄

• I₁ + I₂ = I₃ + `5/2`I₄

• I₁ + I₃ < I₂ + I₄

• I₁ = I₂ = I₃ > I₄

Answer 1

I₁ = I₂ = I₃ > I₄

Explanation:

Let the masses of 4 bodies are M and radius = R

I₁ = `1/2` MR²

I₂ = `1/2` MR²

I₃ = `1/2` MR²

I₄ = `2/5` MR²

So, I₁ = I₂ = I₃ > I₄