Question

A particle of mass $m$ is moving with a velocity $\overrightarrow{v}$ makes a head on elastic collision with another particle of same mass initially at rest. The velocity of the first particle after the collision will be

• A. $\overrightarrow{v}$
• B. $-\overrightarrow{v}$
• C. $-2\overrightarrow{v}$
• D. Zero

Answer 1

Answer: (A)

$\overrightarrow{v}$

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

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

$P_2=0$

$P_i=mv+0=mv$

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

$P_i=P_f$

$mv=m(v_1+v_2)$

$v=v_1+v_2$

collision is elastic $e=1$

$e=\frac{v_1-v_2}{v}=1$

$v_1=v$ and $v_2=0$

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