If earth contracts to half its radius, What would be the length of the day?

 Answer: If earth contracts to half its radius, the moment of inertia of the earth will become one forth as 

I' = 2/5 M (R/2)^2

I' = 2/5 MR^2/4

since L = I ω= constant, therefore the angular velocity of the earth will becomes four times.

i.e ω' = 4ω

2π/T' = 4*2π/T

T ' = T/4 = 24/4 = 6 hours.

Then, The earth will complete one rotation about its axis in 6 hours instead of 24 hours. Hence the day will be of 6 hours.