Two bodies of mass m and 9m are placed at a distance R . The...

Let the gravitational field at point $Q$ is zero. Therefore, we can write

\left(\dfrac{- Gm}{{x}^{2}}\right) + \left(\dfrac{- G \times 9m}{{\left(R - x\right)}^{2}}\right) = 0 ⇒ \dfrac{{\left(R - x\right)}^{2}}{{x}^{2}} = 9 ⇒ x = \dfrac{R}{4}$</p><p>Now, net gravitational potential at point$Q$will be</p><p>${V}_{net} = \left(\dfrac{- Gm}{x}\right) + \left(\dfrac{- G \times 9m}{R - x}\right) = \left(\dfrac{- Gm}{\dfrac{R}{4}}\right) + \left(\dfrac{- G \times 9m}{\dfrac{3R}{4}}\right) = \dfrac{- 16Gm}{R}