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JEE Main 2023 (10 Apr, Shift 1) · Angular Momentum & its Conservation

Angular Momentum & its Conservation question from JEE Main 2023 (10 Apr, Shift 1)

Q39JEE Main 2023 · 10 APR · SHIFT 1Medium

Angular Momentum & its Conservation

If the earth suddenly shrinks to $\frac{1}{64}$ th of its original volume with its mass remaining the same, the period of rotation of earth becomes $\frac{24}{x}$ h. The value of x is __________.

Numerical answer type. Work it out, then open the answer.

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Answer: 16

Volume $\frac{1}{64}$ means $R'=\frac R4$ ; $T\propto I\propto R^2$ (L conserved).
$T'=24\times\frac{1}{16}=\frac{24}{16}$ h
So $x=16$ .

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