A ball of mass 0.5kg moving at 10ms ^ -1 collides with another ball of equal mass at rest. If the two balls…

Analyze the question: A moving ball hits a stationary ball of the same mass, and they stick together (move off together). This is a perfectly inelastic collision, so we use conservation of linear momentum.

Concept: In a collision with no external force, total momentum before = total momentum after.

m₁u₁ + m₂u₂ = (m₁ + m₂)v

Solution:

Given:

• m₁ = 0.5 kg, u₁ = 10 m/s
• m₂ = 0.5 kg, u₂ = 0 (at rest)

Momentum before the collision: (0.5 × 10) + (0.5 × 0) = 5 kg m/s

Momentum after the collision: (0.5 + 0.5)v = 1.0v

Equate them: 1.0v = 5 v = 5 m/s

Answer: The common velocity is 5.0 m/s, which is option C.

Tip: When two equal masses stick together, the mass doubles, so the velocity is halved. Here, 10 ÷ 2 = 5 m/s. Check that your answer is less than the initial velocity, because momentum is shared between more mass. Be careful not to confuse this with an elastic collision, where equal masses would exchange velocities.