Answer the following questions related to the sign of mechanical energy for bodies moving under gravity of a planet of mass M and radius R.
(a) What is meant by gravitational potential energy of a body of mass m located at a distance r from the centre of the planet? State its sign and give the reason.
(b) A particle is said to move in a bound orbit around the planet when its total mechanical energy is negative. Give a reasoned explanation showing how the sign of the total mechanical energy decides whether the trajectory is bound or unbound.
(c) A body is projected from the surface of the planet just enough to come to rest at an infinite distance. State the magnitude and sign of the total mechanical energy of the body during its entire motion and justify your answer.