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The 'e' Equation

Particle A ma...

Question

Particle A makes perfectly elastic collision with another particle B at rest. They fly apart in opposite direction with equal speeds. If their masses are $m_{A}$ and $m_{B}$ respectively. Then

A

2 m_{A} = m_{B}

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B

m_{A} = 3 m_{B}

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C

4 m_{A} = m_{B}

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D

\sqrt{3} m_{A} = m_{B}

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Solution

The correct option is B $m_{A} = 3 m_{B}$
$_{i} = k_{i} f o r V_{B} = 0_{f} =_{f} f o r V_{B} = V_{f (A)} = (\frac{m_{A} - m_{B}}{m_{A} + m_{B}}) U_{A} + (\frac{{2 m}_{A}}{m_{A} + m_{B}})_{i (B)} ∵ (\frac{{2 m}_{A}}{m_{A} + m_{B}})_{i (B)} = 0 \Rightarrow_{f (A)} = (\frac{m_{A} - m_{B}}{m_{A} + m_{B}}) U_{A}_{f (B)} = (\frac{{2 m}_{A}}{m_{A} + m_{B}}) U_{A} (\frac{m_{A} - m_{B}}{m_{A} + m_{B}}) = (\frac{{2 m}_{A}}{m_{A} + m_{B}}) \Rightarrow m_{A} = 3 m_{B}$

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