The masses and radii of earth and moon are M1,R1 and M2,R2 respectively. Their centers are at a distance d apart. Find the minimum speed with which a particle of mass m should be projected from a point midway between the two centers so as to escape to infinity.

Answer onQuestion #41093, Physics, Mechanics | Kinematics | DynamicsQuestion:The masses and radii of the earth and moon are M1, R1 and M2, R2 respectively. Their centres are at distance d apart. The minimum speed with which a particle of mass m should be projected from a point midway the two centres so as to escape to infinity is :-Answer:The law of conservation of energy:푇+푈=푐표푛푠푡where 푇=푚푣22iskinetic energy, 푚-mass, 푣–speed, 푈=−퐺푚푀푟ispotential energy,푟is distance to the center of second body.Therefore:−퐺푀1푚푑2−퐺푀2푚푑2+푚푣22=0+0+0푣2=4퐺푑(푀1+푀2)푣=√4퐺푑(푀1+푀2)Answer: 푣=√4퐺푑(푀1+푀2)