Question

two Small bodies of masses 2.00 kg and 4.00 kg are kept at rest at a separation of 2.0 m. Where should a particle of mass 0.10 kg be placed to experience no net grvitational force from these bodies ? The particle is placed at this point. What is the gravitational potential energy of the system of three particles with usual referene level?

Answer 1

Let 0.1 kg mass, is x m from 2 kg mass and (2-x) m from 4 kg mass.
$\therefore \frac{2\times 0.1}{x^2}=-\frac{4\times 0.1}{(2-x{)}^2}$
$or\frac{0.2}{x^2}=\frac{0.4}{(2-x{)}^2}or\frac{1}{x^2}=\frac{2}{(2-x{)}^2}or(2-x{)}^2=2x^{2}0r2-x=\sqrt{2}xorx(\sqrt{2}+1)=2orx=\frac{2}{2.414}$
= 0.83 m from 2 kg mass.