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A particle of mass $m_{2}$ is at rest. Another particle of mass $m_{1}$ hits it. Collision is one-dimensional and elastic. Suffix $' f'$ represents final and $' i'$ represents initial in the following.
List-I List-II
a) The curve in the figure, which is the graph of the velocity ratio $v_{1 f} / v_{1 i}$ versus the mass ratio $m_{1} / m_{2}$ p) A
b) The value of the intercept of the graph $v_{1 f} / v_{1 i}$ versus the mass ratio $m_{1} / m_{2}$ with the vertical axis is q) C or D
c) The maximum value taken by the graph of $v_{2 f} / v_{1 i}$ versus $m_{1} / m_{2}$ is r) B
d) The curve that is the graph of the velocity ratio $v_{2 f} / v_{1 i}$ versus $m_{1} / m_{2}$ is s) 0
t) -1
u) 2

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a – r; b – t; c – u; d - p

a – p; b – q; c – r; d – s

a – q; b – r; c – s; d - t

a – p; b – t; c – q; d - r

answer is A.

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Detailed Solution

A) If $\frac{m_{1}}{m_{2}} \to 0 \Rightarrow m_{1} \to 0$
Then $v_{2 f} \to 0$ and $v_{1 f} = - v_{1 i}$
$∴ \frac{v_{1 i}}{v_{1 f}} = - 1$
When $\frac{m_{1}}{m_{2}} \to \infty \Rightarrow m_{1} \to \infty$
Then $v_{2 f} \to 2 v_{1 i}$ and $v_{1 f} \to v_{1 i}$
$∴ \frac{v_{1 f}}{v_{1 i}} = 1$
$∴$ Correct graph is (B)
B) From above discussion, the answer is – 1
C) When $\frac{m_{1}}{m_{2}} \to \infty, \frac{v_{2 f}}{v_{1 i}} \to 2$

D) $\frac{v_{2 f}}{v_{1 i}} \to 0$ if $m_{2}$ is massive $\Rightarrow w h e n \frac{m_{1}}{m_{2}} \to 0$
$\frac{v_{2 f}}{v_{1 i}} \to 2$ if $m_{2}$ is light $\Rightarrow w h e n \frac{m_{1}}{m_{2}}$ is large

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