Question

Using expression for change in potential energy, show that gravitational potential energy of the system of object of mass m and the Earth with separation of r is, \(-\frac{GMm}{r}\)

Answer 1

1. Change in P.E. for a system of Earth and mass is given by,

∆U = GMm \((\frac{1}{r_i}-\frac{1}{r_f})\)

2. For gravitational force, point of zero potential energy is taken to be at r = ∞.

3. Hence, U(r_i) = 0 at r_i = ∞

Final point r_f is the point where the potential energy of the system is to be determined.

4. At r_f = r

This is gravitational potential energy of the system of object of mass m and Earth of mass M having separation r (between their centres of mass).