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Question

Two stationary particles of masses M1 and M2 are at distance d apart. A third particle, lying on the line joining the particles, experiences no resultant gravitational force. The distance of this particle from M1 is
  1. d(M2M1M2)
  2. d(M1M1+M2)
  3. d(M1M1M2)
  4. d(M1M1+M2)

A
d(M1M1+M2)
B
d(M2M1M2)
C
d(M1M1M2)
D
d(M1M1+M2)
Solution
Verified by Toppr

Force on m towards M1,
F1=GM1mr2
Force on m towards M2,
F2=GM2m(dr)2
As there is no resultant force
F1=F2
GM1mr2=GM2m(dr)2
(drr)2=M2M1
dr1=M2M1
dr=M2+M1M1
r=d[M1M1+M2]

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