Consider the Earth to be a perfect sphere of radius R rotating with an angular velocity . If the acceleration due to gravity at a small height h ( h R ) above the North Pole is equal to the acceleration due to gravity on the surface of the Earth at the equator, then the value of h is : (where g is the acceleration due to gravity at the surface of the poles)

Step-by-step solution

The acceleration due to gravity at the surface of the Earth at the poles is g . At a small height h ( h R ) above the North Pole, the acceleration due to gravity is given by the approximation: g_h = g (1 - 2h R ) The acceleration due to gravity on the surface of the Earth at the equator is reduced due to the Earth's rotation: g_ eq = g - R ^2 According to the given condition, g_h = g_ eq : g (1 - 2h R ) = g - R ^2 g - 2hg R = g - R ^2 2hg R = R ^2 h = R^2 ^2 2g Answer: R^2 ^2 2g