Question

Let I₁ and I₂ be the moments of inertia of two bodies of identical geometrical shape. If the first body is made of aluminium and the second of iron, then ____________.

Options

• I₁ < I₂

• I₁ = I₂

• I₁ > I₂

• `"I"_1 = "I"_2/2`

Answer 1

Let I₁ and I₂ be the moments of inertia of two bodies of identical geometrical shape. If the first body is made of aluminium and the second of iron, then I₁ < I₂.

Explanation:

I is always proportional to mass and radius of the body. Here, two bodies having same shape and same radius are given.

`therefore "I is directly proportional to mass of the body."`

`"I" prop "M" and "I" prop rho  "V"`

But V = constant

`therefore "I" prop rho`

`therefore "I"_1/"I"_2 = rho_1/rho_2 = rho_("A"l)/rho_ "iron"`

`"But"  rho_("A"l) < rho_"iron"`

`therefore "I"_1 < "I"_2`