In a one-dimensional collision between two particles, their relat… - Vidyadip

MCQ

In a one-dimensional collision between two particles, their relative velocity is ${\vec v_1}$ before the collision and ${\vec v_2}$ after the collision

A
$\vec v_1 = \vec v_2$ if the collision is elastic
B
$\vec v_1 = -\vec v_2$ if the collision is elastic
C
$\vec v_1 = -k \vec v_2$ in all cases, where $k \geq 1$
✓
Both $(B)$ and $(C)$

✓

Answer

Correct option: D.

Both $(B)$ and $(C)$

d
As shown in figure taking one body is rest for simplicity After collisionv $_{1}=\frac{m_{2}-m_{1}}{m_{1}+m_{2}} v \rightarrow(1)$

$v_{2}=\frac{2 m_{1}}{m_{1}+m_{2}} \rightarrow(i i)$

where $v=$ initial velocity of body $A$ Initial relative velocity of $A$ $w.r.t$ $\mathrm{B}$ $v_{A B}=v-0=v$

after collision relative velocity of $\vec{A} .$ w.r.t $\vec{B}$ $v_{A B}=-v_{1}-\left(+v_{2}\right)$

using $(1)$ and $(2)$ $=\frac{-\left(m_{2}-m_{1}\right) v}{m_{1}+m_{2}}-\frac{2 m_{1}}{m_{1}+m_{2}} v$

$=\frac{-m_{1}-m_{2}}{\left(m_{1}+m_{2}\right)} v=-v$

relative velocity changes $v$ to $-v$

in case of other collision relative velocity relation is not determined.

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