Question

One dimension. In the figure, two point particles are fixed on an x axis separated by distance d. Particle A has mass m_A and particle B has mass 6.00 m_A. A third particle C, of mass 73.0 m_A, is to be placed on the x axis and near particles A and B. In terms of distance d, at what x coordinate should C be placed so that the net gravitational force on particle A from particles B and C is zero?

Answer 1

First find the gravitational pull of B on A

F (b) = G m1 m2 / d^2

F (b) = G (mA)(6mA) / d^2

F (b) = 6 G mA^2 / d^2

If net gravitational force is to be zero, the pull of particle C must equate the force of B

F (c) = G m1 m2 / d' ^2

F (c) = G mA x 73mA / d' ^2

F (c) = 73 G mA^2 / d' ^2

Equating;

F (b) = F (c)

6 G mA^2 / d^2 = 73 G mA^2 / d' ^2

6 / d^2 = 73 / d' ^2

( d' / d )^2 = 73 / 6 = 12.17

=>

d' / d = +3.49 or -3.49

d' = -3.49 d ...... since C gotta be on the other side of displacement