Question

A body of mass 2 kg is moving with a velocity v collides inelastically with another body of mass 4 kg at rest. What will be their combined velocity?
1. v/3
2. v/2
3. v
4. v/4

Answer 1

Correct Answer - Option 1 : v/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.

CALCULATION:

Given that m₁ = 2 kg; m₂ = 4kg; now

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.

m1u1 + m2u2 = m1v1 + m2v2 

• since the collision is inelastic, both the body will have the same velocity v' after the collision.

2 × v + 4 × 0 = 2 v' + 4 v'

2v = 6v'

v' = v/3

So the correct answer is option 1.