Gravitational Potential Energy

Gravitation of Class 11

Gravitational Potential Energy

  1. The expression Ug = mgh for gravitational potential energy is valid only near the surface of the earth, where one can assume that the force of gravity is constant.
  2. Now we obtain the potential energy function by considering the variation of the force of gravity.
  3. We know that the change in potential energy between two points is given by the negative of the work done by the conservative force:
  4. UB − UA = − Gravitational Potential Energy.ds(11.12)
  5. Since the force of gravity is central and spherically symmetric, therefore, we can express,
  6. Gravitational Potential Energyc.dGravitational Potential Energy = −Fr dr
  7. because Gravitational Potential Energyc = − FrNewton's Law Of Gravitation and dGravitational Potential Energy = drNewton's Law Of Gravitation
  8. Therefore,UB − UA = Gravitational Potential Energydr
  9. According to Newton's law of gravitation
  10. Fr = GMm/r2
  11. ∴UB − UA = GMmGravitational Potential Energy
  12. orUB = UA + GmGravitational Potential Energy
  13. It we assume zero level of potential energy at infinity,
  14. i.e. UA = 0 as rA → ∞. Then
  15. U = −GMm/r  (11.13)
  16. The above equation gives the potential energy of a particle of mass m separated from the center of earth by a distance r.
Talk to Our counsellor