Question

Masses and radius of the earth and moon are M₁, R₁ and M₂, R₂ respectively. The distance between their centers is d. With what velocity an object of mass m should be projected from the mid-point between them so that it may escape?

(a) \(2\sqrt{\frac{G}{d}(M_1+M_2)}\)

(b)\(2\sqrt{\frac{2G}{d}(M_1+M_2)}\)

(c) \(2\sqrt{\frac{Gm}{d}(M_1+M_2)}\)

(d) \(2\sqrt{\frac{GM}{d}\frac{M_1+M_2}{R_1+R_2}}\)

Answer 1

Correct option is (a)  \(2\sqrt{\frac{G}{d}(M_1+M_2)}\)