A ball of mass m moving at velocity u collides with another ball of equal mass at rest. If the two balls move…

Analyze the question: A moving ball hits an identical ball that is at rest. After the collision they stick together (move off together), so this is a perfectly inelastic collision. We need their common velocity.

Concept: In any collision where no external force acts, the principle of conservation of linear momentum applies:

Total momentum before = Total momentum after

Solution:

Before the collision:

• Ball 1: mass m, velocity u, so momentum = mu
• Ball 2: mass m, velocity 0, so momentum = 0
• Total momentum = mu

After the collision (both balls move together with common velocity v):

• Total mass = m + m = 2m
• Total momentum = 2m × v

Applying conservation of momentum:

mu = 2mv

Divide both sides by m:

u = 2v

v = u/2

Answer: The common velocity is u/2, which is option B.

Why the other options are wrong:

• A and E contain symbols (v, m) that don't belong in the final expression. The mass cancels out.
• C (u) would mean no loss of speed even though the mass doubled, which is impossible.
• D (2u) would mean the velocity increased, which violates momentum conservation.

Exam tip: For "stick together" problems with equal masses, the common velocity is always half the initial velocity of the moving body. In general, for a mass m₁ hitting a stationary mass m₂ and sticking: v = m₁u / (m₁ + m₂). Also remember that kinetic energy is not conserved in such collisions, only momentum is.