Question

Two particles moving initially in the same direction undergo a one dimensional, elastic collision. Their relative velocities before and after collision are $\overrightarrow{v_1}$ and $\overrightarrow{v_2}$. Then :

• A. $\left|\overrightarrow{v_1}\right|=\left|\overrightarrow{v_2}\right|$
• B. $\overrightarrow{v_1}=-\overrightarrow{v_2}$ only if the two are of equal mass
• C. $\overrightarrow{v_1}=-\overrightarrow{v_2}={\left|\overrightarrow{v_1}\right|}^2$
• D. $|\overrightarrow{v_1}.\overrightarrow{v_2}|={\left|\overrightarrow{v_1}\right|}^2$

Answer 1

Answer: (A), (C), (D)

The correct options are
A $\left|\overrightarrow{v_1}\right|=\left|\overrightarrow{v_2}\right|$
C $\overrightarrow{v_1}=-\overrightarrow{v_2}={\left|\overrightarrow{v_1}\right|}^2$
D $|\overrightarrow{v_1}.\overrightarrow{v_2}|={\left|\overrightarrow{v_1}\right|}^2$

Because the collision is elastic, option A is correct.

But option B is incorrect as a vector cannot be equated to a scalar.