Observe the figure and answer the questions :[Figure: two spheres of masses m1 and m2 separated by a distance d, with equal forces F shown acting on each, directed towards the other.](a) State Newton’s universal law of gravitation.(b) If the distance…

Answer: (b) It becomes one-ninth of the original force; (c) it becomes double.

(a) Every object in the universe attracts every other object with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres: \(F = G\dfrac{m_1 m_2}{d^2}\). The force acts along the line joining the centres.

(b) \(F \propto \dfrac{1}{d^2}\). If the distance becomes 3d, the force becomes \(\dfrac{1}{3^2} = \dfrac{1}{9}\) of its original value.

(c) \(F \propto m_1 m_2\). If the mass of one body is doubled, the product of the masses is doubled, so the gravitational force becomes twice as large.