A spherical ball of mass `m_(1)` collides head on with another ball of mass `m_(2)` at rest . The collision is elastic . The fraction of kinetic energy lost by `m_(1)` is `:`

Options

A. `(4m_(1)m_(2))/((m_(1)+m_(2))^(2))`
B. `(m_(1))/(m_(1)+m_(2)`
C. `(m_(2))/(m_(1)+m_(2)`
D. `(m_(1)m_(2))/((m_(1)+m_(2))^(2))`

Answer

A

Explanation

`u=v_(1)+(m_(2))/(m_(1))v_(2) ....(1)`
`v_(2)-v_(2)=u .....(2)`
`(K_(f_(1))-K_(i_(1)))/(K_(i_(1)))=1-((v_(1))/(u))^(2)=(4m_(1)m_(2))/((m_(1)+m_(2))^(2)) Ans. (A)`