Two masses m1 and m2 collide, the ratio of change of their respective velocities will be proportional to what? Options are 1. m1/m2. 2. (m1/m2)^-1/2 3. m2/m1 4. (m2/m1) ^-1/2

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Solution

Dear Student,

$l e t t h e i n i t i a l v e l o c i t y b e u a n d u' a n d t h e f i n a l v e l o c i t y b e v a n d v' v = \frac{m 1 - m 2}{m 1 + m 2} u + \frac{2 m 2}{m 1 + m 2} u' v' = \frac{2 m 1 u}{m 1 + m 2} - \frac{m 1 - m 2}{m 1 + m 2} u' \frac{v - u}{v' - u'} = \frac{\frac{m 1 - m 2}{m 1 + m 2} u + \frac{2 m 2}{m 1 + m 2} u' - u}{\frac{2 m 1 u}{m 1 + m 2} - \frac{m 1 - m 2}{m 1 + m 2} u' - u'} = \frac{- m 2 u + 2 m 2 u' - m 2 u}{2 m 1 u - m 1 u' - m 1 u'} = \frac{2 m 2 (u' - u)}{2 m 1 (u - u')} = \frac{- m 2}{m 1} o p t i o n 3 R e g a r d s$

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