A body of mass `2 kg` moving with a velocity `3 m//s` collides with a body of mass `1 kg` moving with a velocity of `4 m//s` in opposite direction. If the collision is head on and completely inelastic, then

Options

A. both particles move together with velocity `(2/3) m//s`
B. the momentum of system is `2 kg m//s` throughout
C. the momentum of system is `10 kg m//s`
D. the loss of `KE` of system is `(49//3) J`

Answer

A, B, D

Explanation

In completely inlastic collision bodies coalesce
`m_(1)u_(1)-m_(2)u_(2)=(2+1), V,V=2/3m//s`
Net momentum of system `P=m_(1)u_(1)=m_(2)u_(2)`
`2xx3-1xx4=2kgm//s`
Lose in `KE=1/2m_(1)u_(1)^(2)+1/2m_(2)u_(2)^(2)-1/2(m_(1)+m_(2))V^(2)`
`=1/2xx2xx(3)^(2)+1/2xx(1)xx(4)^(2)-1/2xx(2+1)x(2/3)^(2)`
`=9+8-2/3=17=49/3J`