If the earth suddenly contracts to one third of its present radius without change in its mass, the length of the day would be shortened by

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$\frac{8}{3} h o u r s$

$\frac{64}{3} h o u r s$

answer is D.

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Detailed Solution

$I_{1} W_{1} = I_{2} W_{2} \Rightarrow \frac{R^{2}}{T_{1}} = \frac{R^{2}}{9 T_{2}} \Rightarrow T_{2} = \frac{T_{1}}{9}$
$Δ T = (T_{1} - \frac{T_{1}}{9}) = \frac{8 T_{1}}{9} = \frac{64}{3} h r s$

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