If the earth shrinks such that its density becomes `8` times to the present values, then new duration of the day in hours will be

Options

A. 24
B. 12
C. 6
D. 3

Answer

C

Explanation

Given `m_(1)=m_(2)impliesV_(1)d_(1)=V_(2)d_(2)`
`impliesR_(1)^(3)d_(1)=R_(2)^(3)d_(2)impliesR_(1)=2R_(2)`
From law of conservation of angular momentum
`I_(1)omega_(1)=I_(2)omega_(2)=(T_(2))/(T_(1))=((R_(2))/(R_(1)))^(2)`