JEE Advanced Model Paper 2 with solutions for online practice

Let V be the velocity of body Q after the collisions.
From the principle of conservation of linear momentum, we have
mu = mυ + (2m) V or u - υ = 2V (1)
The conservation of kinetic energy gives

1

2

mυ2 =

1

2

mυ2 +

1

2

(2m)V2
Or u2−υ2 = 2V2 (2)
Using Eq (1) in Eq (2), we have Or 2 (u + υ) = 2V (3)
From Eqs. (1) and (3), we get V = -u/3.
Using v =-u/3 in Eq. (1), we get V = 2u/3.