Two particles A and B with masses m and 3m respectively, moving towards each other with a speed of 4u and u respectively. Find the expression of their speed after collision in terms of u and e. Given that V of B =2u, show that e=3/5.

Step 1: Define initial conditions and set up equations for conservation of momentum and coefficient of restitution.
Let the direction of particle A's initial motion be positive.

• Mass of particle A: $m_A = m$
• Mass of particle B: $m_B = 3m$
• Initial velocity of particle A: $u_A = 4u$
• Initial velocity of particle B: $u_B = -u$ (since it's moving towards A)
• Final velocity of particle A: $v_A$
• Final velocity of particle B: $v_B$
• Coefficient of restitution: $e