Question

A ball of mass 10 kg is moving with a velocity of 10 m/s. It strikes another ball of mass 5 kg, which is moving in the same direction with a velocity of 4 m/s. If the collision is elastic, then their velocities after collision will be respectively

• A. 12 m/s, 6 m/s
• B. 12 m/s, 25 m/s
• C. 6 m/s, 12 m/s
• D. 8 m/s, 20 m/s

Answer 1

Answer: (C)

Since, collision is elastic momentum remains conserved, hence we have Momentum before collision = Momentum after collision Initially,
$ p={{m}_{1}}{{u}_{1}}+{{m}_{2}}{{u}_{2}}=10\times 10+5\times 4=120 $ ..(i)
Final, $ p={{m}_{1}}{{v}_{1}}+{{m}_{2}}{{v}_{2}}=10{{v}_{1}}+5{{v}_{2}} $ ..(ii)
Equating Eqs. (i) and (ii), we get
$ 10{{v}_{1}}+5{{v}_{2}}=120 $
$ \Rightarrow $ $ 2{{v}_{1}}+{{v}_{2}}=24 $ ..(iii)
Since collision is elastic relative velocity remains unchanged in magnitude but is reversed in direction,
$ e=1=\frac{{{v}_{2}}-{{v}_{1}}}{{{u}_{1}}-{{u}_{2}}} $
$ \Rightarrow $ $ 10-4={{v}_{2}}-{{v}_{1}} $ ..(iv)
$ \therefore $ $ {{v}_{2}}-{{v}_{1}}=6 $
Solving Eqs. (iii) and (iv), we get
$ {{v}_{1}}=6m/s,{{v}_{2}}=12m/s $