A student incorrectly uses the approximate formula g' = g (1 - 2h R ) to calculate the acceleration due to gravity at a height h above the earth's surface (where R is the radius of the earth). At a particular height, this formula predicts that the weight of a body will become zero. What is the true weight of the body at this height, if its weight on the surface of the earth is W ?

Step-by-step solution

The approximate formula for acceleration due to gravity at a height h is g' = g (1 - 2h R ) . According to the question, this formula predicts zero weight, so g' = 0 . 1 - 2h R = 0 h = R 2 The true acceleration due to gravity at a height h is given by the exact formula: g_h = g (1 + h R )^2 Substituting h = R 2 : g_h = g (1 + 1 2 )^2 = g ( 3 2 )^2 = 4g 9 Therefore, the true weight of the body is W_ true = m g_h = 4 9 mg = 4W 9 . Answer: 4W 9