Two small spherical bodies, A and B, are placed in deep space, free from any external fields. Body A has mass m and charge Q . Body B has mass 2m and charge 2Q . They are initially held at rest at a center-to-center distance of r₀ . They are then released. Assuming the electrostatic force is greater than the gravitational force, what is the kinetic energy of the lighter body A when the separation between them becomes

Step-by-step solution

The initial potential energy of the two-body system is: U_i = k(Q)(2Q) r₀ - G(m)(2m) r₀ = 2kQ^2 r₀ - 2Gm^2 r₀ The final potential energy when the separation is 2r₀ is: U_f = k(Q)(2Q) 2r₀ - G(m)(2m) 2r₀ = kQ^2 r₀ - Gm^2 r₀ By conservation of mechanical energy, the total kinetic energy K acquired by the system is equal to the decrease in potential energy: K = U_i - U_f = kQ^2 r₀ - Gm^2 r₀ = 1 r₀ (kQ^2 - Gm^2) Since the system is initially at rest and no external forces act on it, linear momentum is conserved. The mag