Two particles, one heavy and the other light, placed at 50 cm from each other, are under the influence of gravitational force of one another. If mass of the heavier particle is 4 kg and its acceleration under the influence of gravitational force is 5 10⁻¹⁰ ms⁻² , find the mass of the lighter particle.

Step-by-step solution

Let the mass of the heavier particle be M and the mass of the lighter particle be m . Given: M = 4 kg Distance between the particles, r = 50 cm = 0.5 m Acceleration of the heavier particle, a_M = 5 10⁻¹⁰ ms⁻² Universal gravitational constant, G 6.674 10⁻¹¹ N m^2/kg^2 The gravitational force exerted by the lighter particle on the heavier particle is: F = G M m r^2 According to Newton's second law, the force on the heavier particle is also given by: F = M a_M Equating the two expressions for force: M a_M = G M m r^2