Question

Are the velocity change of two respective objects involved in a collision always equal?

Answer 1

No, not always but it's true if the masses of objects are equal

Explanation:

What is always true is that linear momentum of objects colliding each other is always conserved irrespective of type of collision where elastic or inelastic.

The linear momentum of an object is the product of its mass & velocity. Let the two objects of mass `m_1` & `m_2` collide each other with initial velocities `u_1` & `u_2` in a given direction. If `v_1` & `v_2` are respective velocities in the same direction after collision then

By the law of conservation of momentum,

`m_1u_1+m_2u_2=m_1v_1+m_2v_2`

`m_1(u_1-v_1)=m_2(v_2-u_2)`

If `m_1=m_2` then we have

`(u_1-v_1)=(v_2-u_2)`

`\text{change in velocity of object 1}=\text{change in velocity of object 2}`

change in the velocity of two colliding objects will be equal in magnitude only if the objects have equal mass