Leaving the distance between the 97 kg and the 548 kg masses fixed, at what distance from the 548 kg mass (other than infinitely remote ones) does the 69.7 kg mass experience a net force of zero?

0.70 d

Explanation:

m1 = 97 kg

m2 = 548 kg

m = 69.7 kg

Let the distance between m1 and m2 is d.

Let m be placed at a distance s from m2 so that the net force on m is zero.

Force between m1 and m is balanced by force between m and m2

G m1 x m / (d - s) ^2 = G m x m2 / s^2

m1 / (d - s) ^2 = m2 / s^2

97 / (d - s) ^2 = 548 / s^2

(d - s) ^2 / s^2 = 97 / 548

(d - s) / s = 0.42

d - s = 0.42 s

d = 1.42 s

s = 0.70 d