1. Two particles of maasses m1 and m2 seperated by a distnace (d) are coming towards each other by their mutual gravitational attraction. Find the direction and magnitude of their relative acceleration. Also find the ratio of their mutual attraction at any instant.

Let v be the velocity of approach of two bodies at distance r apart . The reduced mass of the system of the two particles

1/u = 1/ m1 + 1/m2 ,

u = m1 m2 / m1 + m2

According to law of conservation

-Decrease in potential energy = Increase in kinetic energy

-(Gm1 m2 /r ) = 1/2 uv2

Gm1 m2 /r =1/2 (m1 m2 / m1+m2 ) v2

v = (2G (m1 m2 )/r )-1/2