A ball of mass 0.5kg moving at 10ms⁻¹ collides with another ball of equal mass at rest. If the two balls move off together after the impact, calculate their common velocity.
Please note that momentum before impact must be = momentum after impact. This is the law of conservation of momentum.
Mass of ball 1 (M₁) = 0.5kg
Mass of ball 2 (M₂) = 0.5kg
Velocity of ball 1 before collision (V₁) = 10 ms⁻¹
Velocity of ball 2 before collision (V₂) = 0 (since we were told it was at rest)
Common velocity after impact (V₃) =?
Total momentum before impact
= M₁V₁ + M₂V₂
= (0.5 × 10) + (0.5 × 0)
= 5 + 0
Total momentum after impact
= (M₁ + M₂)V₃ (since they sticked together after impact)
= (0.5 + 0.5)V₃
If momentum before impact = momentum after impact, then
5 = V₃
V₃ = 5m/s
Now for the right answer to the above question:
- Option A is incorrect.
- Option B is incorrect.
- C is correct.
- D is not the correct answer.
You may please note these/this:
- The law of conservation of momentum is important here.
- Total momentum before impact = total momentum after impact.
- A body at rest has a velocity of zero.
- If the bodies stick together after the collision, the new mass becomes equal to the simple addition of the masses coming together.
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/ culled from 2021 JAMB-UTME PHYSICS question 4 /