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  4. If the earth shrinks such that its mass does not change but radius decreases to one quarter of its original value then one complete day will take

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Q. If the earth shrinks such that its mass does not change but radius decreases to one quarter of its original value then one complete day will take

WBJEEWBJEE 2008

Solution:

We know that angular momentum of spin $=I \omega$
By the conservation of angular momentum
$\frac{2}{5} M R^{2} \cdot \frac{2 \pi}{T}=\frac{2}{5} M\left(\frac{R}{4}\right)^{2} \cdot \frac{2 \pi}{T'}$
$T'=\frac{T}{16}=\frac{24}{16}=1.5\, h$