If radius of the earth contracts to half of its present value without change in its mass, what will be the new duration of the day?

Explanation

Present angular momentum of earth
`L_(1)=Iomega=(2)/(5)MR^(2)omega`
New angular momentum because of change in radius
`L_(2)=(2)/(5)M((R)/(2))^(2)omega'`
if external torque is zero then angular momentum
must be conserved
`L_(1)=L_(2)`
`(2)/(5)MR^(2)omega=(1)/(4)xx(2)/(5)MR^(2)omega'`
i.e., `omega'=4omega`
`T'=(1)/(4)T=(1)/(4)xx24=6h`