Question

Two bodies with moments of inertia I₁ and I₂ (I₁ > I₂) have equal angular momenta. lf E₁ and E₂ are their rotational kinetic energies respectively, then ____________.

Options

• E₁ > E₂

• E₁ = E₂

• E₁ < E₂

• E₁ = `sqrt2` E₂

Answer 1

Two bodies with moments of inertia I₁ and I₂ (I₁ > I₂) have equal angular momenta. lf E₁ and E₂ are their rotational kinetic energies respectively, then

E₁ < E₂.

Explanation:

L1 = L2

`therefore  "I"_1 omega_1 = "I"_2 omega_2`

`therefore  "I"_1^2  omega _1^2 = "I"_2^2  omega _2^2   "or"  (1/2 "I"_1  omega_1^2) "I"_1 = (1/2 "I"_2  omega _2^2) "I"_2`  or  E₁ I₁ = E₂ I₂

`because "I"_1 > "I"_2 Rightarrow "E"_1 < "E"_2`