At the equator, a person stands on a spring balance. If the speed of earth's rotation is increased by such an amount that the balance reading becomes half the true weight, what will be the length of the day in this case?

Step-by-step solution

The apparent weight of a person at the equator is given by W' = mg - m ^2 R , where m is the mass, g is the acceleration due to gravity, is the angular velocity of the earth, and R is the radius of the earth. Given that the new apparent weight is half of the true weight, W' = mg 2 . Substituting this into the equation: mg 2 = mg - m ^2 R m ^2 R = mg 2 = g 2R The new length of the day T is given by T = 2 . T = 2 2R g = 2 ( 2 R g ) The quantity 2 R g represents the time period of a satellite orbiting close to the ear