The mass and radius of the earth are M_1, R_1and those for the moon are M_2, R_2respectively. The distance between their centers is d with that velocity should an object of mass m be thrown away from the mid-point of the line joining them so that it escapes to infinity ?

The mass and radius of the earth are M_1, R_1and those for the moon ar

1.	The mass and radius of the earth are M_1, R_1and those for the moon are M_2, R_2respectively. The distance between their centers is d with that velocity should an object of mass m be thrown away from the mid-point of the line joining them so that it escapes to infinity ?
Answer» SOLUTION :`implies`The distance between earth and moon is d. SINCE body is in between the line joining between earth and moon isHence, its distance from earth or moon is `d//2` . `implies` Total ENERGY of body having stationary mass m at distance `d//2`due to earth. POTENTIAL energy `U_(1) = -(GM_(1) m)/(d//2) ""....(1)` `implies` Total energy of body having stationary mass m at distance d/2 due to moon Potential energy `U_(2) = - (GM_(2)m)/(d//2) ""...(2)` `:.` Binding energy of body of mass m at the centre of earth, ` = (2Gm)/d [M_(1) +M_(2)]` `implies` Suppose, a body escape to infinity at velocity `v_e.`hence escape energy, `=1/2 mv_(E)^(2) ""...(3)` `:. 1/2 mv_e^2 =(2Gm)/d [M_(1)+M_(2)]` `:. v_(e)= sqrt((4G)/d(M_(1+M_2)))`