Assuming the earth to be spherical, a body stretches a spring by a certain length on the earth's surface at the equator. At what height above the south pole will it stretch the same spring by the exact same length?

Step-by-step solution

The effective acceleration due to gravity at the equator is given by: g_ e = g - ^2 R where g is the acceleration due to gravity at the poles, is the angular velocity of the earth, and R is the radius of the earth. The acceleration due to gravity at a height h above the south pole (where centrifugal force is zero) is: g_ h = g (1 - 2h R ) (assuming h R ) Since the spring is stretched by the same length, the effective gravity at both locations must be equal: g_ e = g_ h g - ^2 R = g - 2gh R ^2 R = 2gh R h = ^2 R^2 2