Question

Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio:

Options

• 2 : 1

• 1 : 2

• `sqrt2:1`

• `1:sqrt2`

Answer 1

`1:sqrt2`

Explanation:

K = `"L"^2/(2"I")`

⇒ L² = 2KI

⇒ L = `sqrt(2"KI")`

`"L"_1/"L"_2 = sqrt("K"_1/"K"_2*"I"_1/"I"_2)`

= `sqrt("K"/"K"*"I"/(2"I"))`

= `1/sqrt2`

⇒ L₁ : L₂ = `1:sqrt2`