A body 'A' moving in a straight line with velocity v makes a collision with a body 'B' initially at rest. After collision, B acquires a velocity of `1.6v`. Assuming the bodies to be perfectly elastic, what is the ratio of the mass of A to that of B? What percentage of A's energy is transferred to B as a result of collision.

Answer

`64%`

Explanation

`COLM = - ((1.6v) - v_(A))/(0 - v) v_(A) = 0.6V` ….(i)
`COLM rArr m_(A)v = m_(A) xx (0.6V) + m_(B) (1.6 v)`
`(m_(A))/(m_(B)) = 4` ….(ii)
`DeltaE_(B) = (1)/(2)m_(B) (1.6 v^(2)) = 0 = 2m_(B) (0.8 v)^(2)`
`K_(A) = (1)/(2) (4m_(B))v^(2) = 2m_(B)v^(2) rArr (DeltaK_(B))/(K_(A)) = 0.64 = 64%`