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

The moment of inertia (If I = 2/5 M${ R }_{ 2 }$) of the earth about its own axis will become one-fourth and so its angular velocity will become four times (L = Iω= constant). Hence, the time period will reduce to one-fourth (T = 2$\pi$/ω to), i.e. 6 hours.