Question

A particle of mass m moving with a velocity v collides with a particle of mass 2m at rest and sticks to it. Velocity of the combined mass equal to?

• A. v
• B. $\frac{v}{2}$
• C. $\frac{v}{3}$
• D. $\frac{v}{4}$

Answer 1

Answer: (C)

$\frac{v}{3}$

Answer 2

Given masses of the particles are, m1 = m and m2 = 2m
Initially the first particle is moving with velocity, v1 = v
And, the second particle is at rest, therefore v2 = 0
The initial momentum of the system is
pi = m1v1 + m2v2 = mv +0 = mv
Now after the collision, both the particles stick together.
The combined mass of the system is (m1 + m2)
Let V be the velocity of the combined mass, then the final momentum of the system is given by
pf = (m1 + m2)V = (m + 2m)V = 3mV
Since there is no external force acting on the system, therefore according to the law of conservation of momentum, initial momentum will be equal to final momentum. i.e.
pi = pf
⇒ mv = 3mV ⇒ V = $\frac{v}{3}$
**Answer. **C