Determine the kinetic energy required to project a body of mass m from the surface of the earth to infinity.

Step-by-step solution

By the principle of conservation of mechanical energy, the total energy of the body at the surface of the earth must be equal to its total energy at infinity. Let K be the required kinetic energy. The initial potential energy at the surface of the earth is U_ i = - GMm R . At infinity, the potential energy is U_ f = 0 . For the minimum kinetic energy required, the final kinetic energy at infinity is zero. K + U_ i = U_ f + K_ f K - GMm R = 0 + 0 K = GMm R We know that the acceleration due to gravity at the surface