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Two bodies have their moments of inertia I₁ and I₂ respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio:

1. 2 : 1
2. 1 : 2
3. √2 : 1
4. 1 : √2

Correct answer: 1 : √2

Solution

The rotational kinetic energy is given by (1/2)Iω². Since the kinetic energies are equal, (1/2)I₁ω₁² = (1/2)I₂ω₂², which simplifies to I₁ω₁² = I₂ω₂². Angular momentum L = Iω, so L₁/L₂ = √(I₁/I₂). If I₁/I₂ = 1/2, then L₁/L₂ = 1/√2.

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