Question

Mass 1 is five times as large as mass 2. Both masses area at rest and are separated by 150 m.

Where could you place a third mass, mass 3, if the net force on mass 3 must be zero?

Answer 1

$F_1=\frac{Gm_3m}{x^2},$

$F_2=\frac{5Gm_3m}{(150-x)^2},$

$F_1=F_2,$

$(150-x)^2=5x^2,$

$x^2+75x-225\cdot 25=0,$

$x=\frac{\sqrt{28125}-75}{2}\approx 46.3$ m from the mass 2.