Question

If earth shrinks to 1/64 of its volume with mass remaining same, duration of the day will be

Moderate

Solution

$Iω = \frac{2}{5} {MR}^{2} ω = constant and V \propto R^{3}$
as v decreases by 64 times R decreases by 4 times and moment of inertia decreases by 16 times and $ω$ increases by 16 times T decreases to 16 times.

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