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**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.**

**A.**** 0.2ms⁻¹**

**B.**** 0.5ms⁻¹**

**C.**** 5.0ms⁻¹**

**D.**** 5.5ms⁻¹**

**QUICK ANSWER…**

**C**

**DETAILS…**

**Please note that momentum before impact must be = momentum after impact. This is the law of conservation of momentum.**

**Data given:**

**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**

**= 5kgm/s**

**Total momentum after impact**

**= (M₁ + M₂)V₃ (since they sticked together after impact)**

**= (0.5 + 0.5)V₃**

**= (1)V₃**

**= 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.**

**KEY-POINTS…**

**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 20****21**** JAMB-UTME ****PHYSICS**** question ****4 ****/**