Two particles mass (m₁ ) and (m₂ ) are kept at rest at (t=0 ). They start attracting each other due to their gravitational pull, then Statement-I: The total momentum of the system is zero at any instant. Statement-II: Both the particles gain equal momentum in opposite direction in equal interval of time as both are acted upon equal and opposite forces.

Step-by-step solution

1. By Newton's third law the internal forces are equal and opposite: ( F ₁₂=- F ₂₁ . ) If ( p ₁, p ₂ ) are momenta, then ( d p ₁ d t = F ₁₂, d p ₂ d t = F ₂₁=- F ₁₂ . ) Add them: ( d d t ( p ₁+ p ₂ )=0 p ₁+ p ₂= constant ) Initially both particles are at rest, so ( p ₁+ p ₂= 0 ). Hence at every later time the total momentum remains zero. This proves Statement I. 2. From the pair of equations above, ( d p ₁ d t =- d p ₂ d t . ) Integrating over any equal time interval gives ( p ₁=- p ₂, ) i.e. they gain equal magnit