A particle A of mass m and initial velocity v collides with a particle B of mass m 2 which is at rest. The…

1. $\frac{{\lambda }_A}{{\lambda }_B}=\frac{1}{2}$
2. $\frac{{\lambda }_A}{{\lambda }_B}=\frac{1}{3}$
3. $\frac{{\lambda }_A}{{\lambda }_B}=2$
4. $\frac{{\lambda }_A}{{\lambda }_B}=\frac{2}{3}$

Solution

$mV=m{V}_A+\frac{m}{2}{V}_B$

$V=V_A+\frac{V_B}{2}------------\text{(i)}$

$V=V_B-V_A------------\text{(ii)}$

$\text{Solving (i) and (ii)}$

$2V=\frac{3V_B}{2}$

$\therefore V_B=\frac{4V}{3}$

$V_A=V_B-V=\frac{V}{3}$

$P_A=\frac{mV}{3}$

$P_B=\frac{m}{2}.\frac{4V}{3}$

$\frac{{\lambda }_A}{{\lambda }_B}=\frac{h\times P_B}{P_A\times h}=\frac{\frac{2mV}{3}}{\frac{mV}{3}}=2$

Asked in: JEE Main 2017 (02 Apr)

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