From law of conservation of momentum
(If there are no external forces acting on the system then)
m1u1+m2u2=m1v1+m2v2
(m1 and m2 are the masses of the 2 given bodies)
(u1 and u2 are the initial velocities of m1 and m2)
(v1 and v2 are the final velocities of m1 and m2 )
Here masses are equal and initial velocities are equal
So,m1=m2 and u1=u2
Here the objects are moving in opposite directions
So,u1=-u2
(or)
-u1=u2
From m1u1+m2u2=m1v1+m2v2,
m1u1+(-m1u1)=m1v+m1v . Since m1=m2 and u1=-u2 v is the common velocity
0=2m1v1
0/2m1=v (Since mass cannot be equal to zero)
0=v
(or)
v=0.

Explanation:
When two equal masses m each moving in the opposite direction with the same speed v collide and stick to each other, the velocity of the combined mass will be zero. This can be explained using the principle of conservation of momentum.

Conservation of Momentum:
According to the principle of conservation of momentum, the total momentum of an isolated system remains constant. That is, the total momentum of the system before the collision is equal to the total momentum of the system after the collision.

Before the Collision:
Let the two equal masses be denoted by m1 and m2. They are moving in opposite directions with the same speed v. Therefore, the momentum of m1 is given by:

p1 = m1 * v

Similarly, the momentum of m2 is given by:

p2 = -m2 * v (since it is moving in the opposite direction)

Therefore, the total momentum of the system before the collision is given by:

p = p1 + p2 = m1 * v - m2 * v = (m1 - m2) * v

After the Collision:
After the collision, the two masses stick together and move with a common velocity v'. Let the combined mass be denoted by M. Therefore, the momentum of the combined mass is given by:

p' = M * v'

Since there is no external force acting on the system, the total momentum of the system after the collision is equal to the total momentum before the collision. That is:

p = p'

Therefore,

(m1 - m2) * v = M * v'

Dividing both sides by M, we get:

v' = (m1 - m2) * v / M

Since m1 = m2 = m (equal masses), we get:

v' = 0

Therefore, the velocity of the combined mass after the collision is zero.

Conclusion:
When two equal masses m each moving in the opposite direction with the same speed v collide and stick to each other, the velocity of the combined mass is zero. This is because of the principle of conservation of momentum, which states that the total momentum of an isolated system remains constant.