two planets of masses m and respectively.have a centre to center separation of r.at what distance from the center of the pianet of mass m do the gravitational force of planets cancel each other???

Answer 1

Assuming you meant masses M and m, then we need at distance d from M,

M/d^2 + m/(r-d)^2 = 0
M(r-d)^2 + md^2 = 0
(M+m)d^2 - 2Mrd + Mr^2 = 0

d = r/2 * (M+√Mm)/(M+m)

just as a sanity check, it's easy to see that d=r/2 when M=m