the radius of earth is reduced to half suddenly ( not due to any external torque) how long will the length of the day be decreased if earth is a perfect sphere???(mi = 2/5mr^2)
Assuming: the earth interior has constant density. A complicated deduction leads to the conclusion that the angular mass (I) is given by I = 3/20 * M * PI * R^2, with M the earth mass and R the radius. The physics law we have to use is conservation of angular momentum: Lfinal = Linit, with L = I x W (W is the angular velocity). The duration of the day will be given in this angular velocity, currently Winitial=24 hours/day. Some substitutions, Rfinal=Rinitial/2, Mfinal=Minitial, and we obtain, Wfinal=Winitial/4. Therefore the duration of the day will be 24 h / 4 = 6 hours.