When a body of mass `m_(1)` moving with uniform velocity `40 ms^(-1)` collides with another body of mass `m_(2)` at rest, then the two together begin to move with uniform velocity of `30 ms^(-1)`. The ratio of the masses (i.e., `m_(1)//m_(2)`) of the two bodies will be

Options

A. `1 : 3`
B. `3 : 1`
C. `1 : 1.33`
D. `1 : 0.75`

Answer

B

Explanation

Initial momentum of the system
`=m_(1)xx40+m_(2) xx0=40 m_(1)`
Final momentum of the system `=(m_(1)+m_(2))xx30`
By the law of conservation of momentum,
Initial momentum = Final momentum
`40 m_(1) =(m_(1)+m_(2))30`
`40 m_(1)-30 m_(1) =30 m_(2)`
`10 m_(1) = 30 m_(2) implies m_(1)/m_(2) =3/1`