• question_answer The masses and radii of the earth and moon are${{M}_{1}},{{R}_{1}}$and${{M}_{2}},{{R}_{2}},$respectively. Their centres are at distance d apart. The minimum speed with which a particle of mass m should be projected from the mid-point between their centres, so that the particle goes out from the gravitational influence of both earth and moon, is A) $2\sqrt{\frac{G({{M}_{1}}+{{M}_{2}})}{md}}$           B) $2\sqrt{\frac{G({{M}_{1}}+{{M}_{2}})}{d}}$C)  $2\sqrt{\frac{G({{M}_{1}}-{{M}_{2}})}{md}}$D) $2\sqrt{\frac{G({{M}_{1}}-{{M}_{2}})}{d}}$

By the Law of conservation of energy $-\frac{G{{M}_{1}}m}{d/2}-\frac{G{{M}_{2}}m}{d/2}+\frac{m{{v}^{2}}}{2}=0$ Where v is the sought velocity $v=2\sqrt{\frac{G({{M}_{1}}+{{M}_{2}})}{d}}$ Hence, the correction option is [b].