see first of all it is not a question of circular motion ...it is from rotational mech.

 

According to law or conservation of angular momentum

 

I₁w₁ = I₂w₂    --(1)

Earth can be considered as a shpere so I = 2/5 Mr²

Now since the radii is halved  I will become I/4

Using this in eqn 1

I*w = I/4*w₂

w₂ = 4w

now w = 2 pi/T

w inc four times so T becomes T/4

so duration of day = 24/4 = 6 hrs