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The 'e' Equation

Two particles...

Question

Two particles moving initially in the same direction undergo a one dimensional, elastic collision. Their relative velocities before and after collision are $_{1}$ and $_{2}$ . Then :

A

∣ ∣_{1} ∣ ∣ = ∣ ∣_{2} ∣ ∣

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B

_{1} = -_{2}

only if the two are of equal mass

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C

_{1} = -_{2} = {∣ ∣_{1} ∣ ∣}^{2}

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D

∣ ∣_{1} ._{2} ∣ ∣ = {∣ ∣_{1} ∣ ∣}^{2}

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Solution

The correct options are
A $∣ ∣_{1} ∣ ∣ = ∣ ∣_{2} ∣ ∣$
C $_{1} = -_{2} = {∣ ∣_{1} ∣ ∣}^{2}$
D $∣ ∣_{1} ._{2} ∣ ∣ = {∣ ∣_{1} ∣ ∣}^{2}$
Because the collision is elastic, option A is correct.
But option B is incorrect as a vector cannot be equated to a scalar.

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