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

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

Tardigrade Admin · Accepted Answer

Applying momentum conservation: 15m+10m=mv1+mv2 25=v1+v2 And (v2 - v1/u1 - u2)=1 ⇒ (v2 - v1/15 - 10)=1 ⇒ v2-v1=5 Solving Eqs. (i) and (ii), we have v2=15ms- 1,v1=10ms- 1

Q. 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

$10 m s^{- 1}$ , $15 m s^{- 1}$

$20 m s^{- 1}$ , $5 m s^{- 1}$

$0 m s^{- 1}$ , $25 m s^{- 1}$

$5 m s^{- 1}$ , $20 m s^{- 1}$

Applying momentum conservation:
$15 m + 10 m = m v_{1} + m v_{2}$
$25 = v_{1} + v_{2}$
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
$v_{2} = 15 m s^{- 1}, v_{1} = 10 m s^{- 1}$

Q. Two perfectly elastic objects A and B of identical mass are moving with velocities 15ms−1 and 10ms−1 respectively, collide along the direction of line joining them. Their velocities after the collision are respectively

10ms−1 , 15ms−1

20ms−1 , 5ms−1

0ms−1 , 25ms−1

5ms−1 , 20ms−1