Question

the kinetic energy needed to project a body of mass M from the Earth surface to infinity is

Answer 1

assume radius of earth is R and mass is M and mass of body is m.
now at infinity the gravitational potential energy will be zero.
As there is only gravity we can apply the conservation of mechanical energy
Now, Initial G.P.E. = -GmM/R    Final G.P.E= 0
U(initial) + K(initial) = U(final) + K(final)
As K(final) should be > or = 0, For Min K(initial) , K(final)=0
Solving you get K(initial min) = GmM/R