A moving body with a mass `m_(1)` strikes a stationary body of mass `m_(2)`. The masses `m_(1)` and `m_(2)` should be in the ratio `m_(1)/m_(2)` so as to decrease the velocity of the first body 1.5 times assuming a perfectly elastic impact. Then the ratio `m_(1)/m_(2)` is

Options

A. 5
B. `1//5`
C. `1//25`
D. 25

Answer

A

Explanation

`m_(1)u=m_(1)(2u)/(3)+m_(2)u` (By condition o linear momentum)
`implies(1)/(3)m_(1)u=m_(2)v`………..(i)
Also e `|(v_(1)-v_(2))|/|(u_(2)-u_(1))|`
`impliesv-(2u)/(3)=uimpliesv=(5)/(3)u`…..(ii)
From (i) and (ii), `(1)/(3)m_(1)u=(5)/(3)m_(2)uimplies(m_(1))/(m_(2))=5`