The masses and radii of the earth and moon are M₁ , R₁ and M₂ , R₂ and respectively, Their centres are at a distance 'd' apart. The minimum speed with which body of mass 'm' should be projected from a distance 2d/3 from the centre of M₁ so as to escape to infinity is

Step-by-step solution

Let the body of mass m be projected from a point P on the line joining the centres of the two bodies. The distance of point P from the centre of M₁ is r₁ = 2d 3 . The distance of point P from the centre of M₂ is r₂ = d - 2d 3 = d 3 . The total gravitational potential energy of the body at point P is the sum of the potential energies due to M₁ and M₂ : U = - G M₁ m r₁ - G M₂ m r₂ U = - G M₁ m 2d 3 - G M₂ m d 3 U = - 3G M₁ m 2d - 3G M₂ m d U = - 3G m 2d (M₁ + 2M₂) For the body to just escape to infinity, its total me