Question

A steel ball of mass 2m suffers one-dimensional elastic collision with a row of three steel balls, each of mass m. If mass 2m has collided with velocity v and the three balls numbered 1, 2, 3 were initially at rest, then after the collision :

• A. balls 1, 2 and 3 would start moving to the right, each with velocity v/3
• B. balls 2 and 3 would start moving to the right, each with velocity v/2
• C. balls 2 and 3 would start moving to the right, each with velocity v
• D. ball 1 and ball of mass 2m would remain at rest

Answer 1

Answer: (C), (D)

The correct options are
C ball 1 and ball of mass 2m would remain at rest
D balls 2 and 3 would start moving to the right, each with velocity v

Since the collision is elastic we can apply law of conservation of momentum and check each option.
For eq, as per option A, applying law of conservation of momentum
$2mv=m\frac{v}{3}+m\frac{v}{3}+m\frac{v}{3}$
$2v=v$ which is not possible , so option A is incorrect
Similarly option B is incorrect
Looking at option C,
$2mv=mv+mv$ which is possible, hence option C is correct
As per option C only ball 1 and ball of mass 2m would remain at rest after collision.

Hence, option D is also correct.