Question

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

Options

• 1 : 2

• 1 : `2sqrt2`

• 2 : 1

• `1 : sqrt2`

Answer 1

Two bodies have their moments of inertia I and 2I respectively about their axes of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio `underline(1 : sqrt2)`.

Explanation:

(kE)₁ = (kE)₂

`therefore 1/2 "I"omega_1^2 = 1/2 (2"I")omega_2^2`

`therefore omega_1^2/omega_2^2` = 2

`therefore omega_1/omega_2 = sqrt2`

Ratio of angular momenta =

`("I"omega_1)/(2"I"omega_2) = 1/2 omega_1/omega_2 = 1/sqrt2`