Question

Two identical balls $A$ and $B$ collide head on elastically. If velocities of $A$ and $B$ before the collision are $+ 0.5\, m/s$ and $- 0.3\, m/s$ respectively, then their velocities after the collision will be :

• A. + 0.5nysand+ 0.3 m/s
• B. - 0.5 m/s and + 0.3 m/s
• C. + 0.3 m/s and - 0.5 m/s
• D. - 0.3 m/s and + 0.5 m/s

Answer 1

Answer: (D)

Momentum and energy both are conserved in elastic collision.
Given, $ {{v}_{A}}=+0.5\,m/s,\,{{v}_{B}}=-0.3\,m/s $
Initial momentum = final momentum
$ {{m}_{A}}{{v}_{B}}+{{m}_{B}}={{m}_{A}}v{{}_{A}}+{{m}_{B}}v{{}_{B}} $
$ \Rightarrow $ $ 0.5+(-0.3)=v{{}_{A}}+v{{}_{B}} $ ?.. (i)
From law of conservation of energy,
$ \frac{1}{2}({{m}_{A}}\,v_{A}^{2}+{{m}_{B}}\,v_{B}^{2})=\frac{1}{2}({{m}_{A}}\,v_{A}^{2}+{{m}_{B}}v_{B}^{2}) $ ?.. (ii)
$ {{(0.5)}^{2}}+{{(-0.3)}^{2}}=v_{A}^{2}+v_{B}^{2} $
From Eqs. (i) and (ii),
we get $ v{{}_{A}}=-0.3\,m/s,\,v{{}_{B}}=+0.5\,m/s $ .
Note: In an elastic collision, velocities after collision get interchanged.