Determine the height above the earth's surface at which the weight of a body decreases to half of its value at the surface. (Let R be the radius of the earth)

Step-by-step solution

The weight of a body at the surface of the earth is W = mg . The weight of the body at a height h above the earth's surface is W_h = mg_h . Given that W_h = W 2 , we have g_h = g 2 . The acceleration due to gravity at a height h is given by g_h = g (1 + h R )^2 . Substituting g_h = g 2 , we get: g 2 = g (1 + h R )^2 (1 + h R )^2 = 2 1 + h R = 2 h R = 2 - 1 h = ( 2 - 1) R