Question

A mass 'm' has velocity 'u'. It collides with another mass '2m' inelastically. Find their combined velocity if initially 2 m mass was at rest.
1. 3u
2. 2u
3. u/2
4. u/3

Answer 1

Correct Answer - Option 4 : u/3

CONCEPT:

• During the collision, the momentum of the system is conserved.
• Momentum Conservation: When in a system, there is no external force then the total momentum (P) of the system will be conserved.

• Momentum: A property of a body in motion that is equal to the product of the body's mass and velocity is called momentum.

P = mv

where P is the momentum of the body, m is the mass of the body, and v is the velocity of the body.

• In an inelastic collision, after collision bodies stick to each other and move combinedly.
• During the collision, the momentum of the system is conserved.

Pinitial = Pfinal 

m1u1 + m2u2 = m1v1 + m2v2 

where u1 is the initial velocity of the first ball, u2 is the initial velocity of the second ball, v1 is the final velocity of the first ball, v2 is the final velocity of the second ball.

CALCULATION:

Given that m1 = m; m2 = 2m; u₁ = u

Now momentum will be conserved in the collision

m1u1 + m2u2 = m1v1 + m2v2

Since the collision is inelastic, both the masses will have the same velocity 'v' after the collision. i.e. v₁ = v₂ = v

m × u + 2m × 0 = m v + 2 mv

mu = 3 mv

v = u/3

So the correct answer is option 4.