Question

Two perfectly elastic objects $A$ and $B$ of identical mass are moving with velocities $15 \, m \, s^{- 1}$ and $10 \, m \, s^{- 1}$ respectively, collide along the direction of line joining them. Their velocities after the collision are respectively

• A. $10 \, m \, s^{- 1}$ , $15 \, m \, s^{- 1}$
• B. $20 \, m \, s^{- 1}$ , $5 \, m \, s^{- 1}$
• C. $0 \, m \, s^{- 1}$ , $25 \, m \, s^{- 1}$
• D. $5 \, m \, s^{- 1}$ , $20 \, m \, s^{- 1}$

Answer 1

Answer: (A)

Applying momentum conservation:
$15m+10m=mv_{1}+mv_{2}$
$25=v_{1}+v_{2}$
And $\frac{v_{2} - v_{1}}{u_{1} - u_{2}}=1$
$\Rightarrow \, \, \frac{v_{2} - v_{1}}{15 - 10}=1$
$\Rightarrow \, \, \, v_{2}-v_{1}=5$
Solving Eqs. (i) and (ii), we have
$v_{2}=15ms^{- 1},v_{1}=10ms^{- 1}$