Question

A ball of mass m moving with velocity V makes a head on elastic collision with a ball of the same mass moving with velocity 2V towards it. Taking direction of V as positive velocities of the two balls after collision are

• A. -V and 2V
• B. 2V and -V
• C. V and -2V
• D. -2V and V

Answer 1

The correct option is D -2V and V

Since There is no external force, we can apply momentum conservation,

Taking the direction of the ball with velocity V positive.

$P_2=-m\left(2V\right)=-2mV$

$P_1=m\left(V\right)=mV$

$P_i=mV-2mV=-mV$

and $P_f=m{v}_1+m{v}_2$

$P_i=P_f$

$-mV=m{v}_2-m{v}_1$

$v_2+v_1=-V$ ...(i)

collision is elastic so e=1

$e=\frac{v_2-v_1}{2V+V}$

$v_2+v_1=3V$ ....(ii)

from 1 and 2

$v_1=-2V$ and $v_2=V$

Hence option D is correct.

we can also conclude that Due to elastic collision of bodies having equal mass, their velocities get interchanged.