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The relation between K.E. of rotation and angular momentum is given by K = L² / 2I. If L₁ : L₂ = √2, then the ratio of their moments of inertia I₁ : I₂ will be:

1. K₁ / K₂ = J₁ / J₂
2. K / K₁ = I / 2I
3. √(K / K₁) = √(I / 2I)
4. 1 / √2

Correct answer: 1 / √2

Solution

Using the given relation K = L² / 2I, if L₁ : L₂ = √2, then I₁ : I₂ must be inversely proportional to the square of L. Hence, I₁ : I₂ = 1 : √2.

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