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

Step-by-step solution

I 1 ω 1 = I 2 ω 2 ρ 1 4 3 π r 1 3 = ρ 2 4 3 π r 2 3 ρ 1 r 1 3 = ρ 2 r 2 3 r 2 = ( ρ 1 ρ 2 ) 1 3 r 1 T = 2 π ω ⇒ T 1 T 2 = I 1 I 2 T 2 = T 1     I 2 I 1 = T 1 ( ρ 1 ρ 2 ) 2 3 = 24 ( 1 4 ) = 6   h