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  4. If the earth were to contract such that its radius becomes one quarter, without change in its mass, the duration of one full day would be

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Q. If the earth were to contract such that its radius becomes one quarter, without change in its mass, the duration of one full day would be

KEAMKEAM 2007

Solution:

As angular momentum is conserved, so
$ I\omega =constant $
$ \therefore $ $ {{I}_{2}}{{\omega }_{2}}={{I}_{1}}{{\omega }_{1}} $
Or $ \frac{2}{5}M{{\left( \frac{R}{4} \right)}^{2}}\times \frac{2\pi }{T}=\frac{2}{5}M{{R}^{2}}\times \frac{2\pi }{24} $
Or $ 16T=24 $
$ \Rightarrow $ $ T=1.5h $