The work done to raise a body of mass m from the surface of the Earth to a certain height h is 3 4 mgR , where R is the radius of the Earth and g is the acceleration due to gravity at the surface. The height h is:

Step-by-step solution

The change in gravitational potential energy when a mass m is raised to a height h from the Earth's surface is given by: W = U = mgh 1 + h R Given that the work done is W = 3 4 mgR , we can equate the two expressions: 3 4 mgR = mgh 1 + h R Cancelling mg from both sides: 3 4 R = h 1 + h R 3 4 R = hR R + h Cross-multiplying gives: 3(R + h) = 4h 3R + 3h = 4h h = 3R Using the incorrect approximation W = mgh would lead to the wrong answer h = 3 4 R . Answer: 3R