A body of mass 2 kg moving with a velocity `3 m//sec` collides with a body of mass 1 kg moving with a velocity of `4 m//sec` in opposite direction. If
A body of mass 2 kg moving with a velocity `3 m//sec` collides with a body of mass 1 kg moving with a velocity of `4 m//sec` in opposite direction. If the collision is head-on perfect inelastic, then
A. both particles will move together with velocity `(2//3) m//sec` after collision
B. the momentum of the system is `2 kg m//sec` throughout
C. the momentum of the system is `10 kg m//sec` throughout
D. The loss in KE of the system is `(49//3)` Joule
1 Answers
Correct Answer - A::B::D
Applying momentum conservation.
`m_(1)u_(1) - m_(2) u_(2) = (m_(1) + m_(2))v`
`2 (3) - 1 (4) = (2 + 1) v`
`rArr v = (2)/(3)` m/sec
Net mometum `= m_(1) u_(1) - m_(2) u_(2)`
`2 (3) - 1 (4) = 2 kg-m//sec`
Loss in `KE = (1)/(2) m_(1) u_(1)^(2) + (1)/(2) m_(2) u_(2)^(2) - (1)/(2) (m_(1) + m_(2)) v^(2)`
`= (1)/(2) xx 2 xx (3)^(2) + (1)/(2) xx (1) xx (4)^(2) - (1)/(2) (2 + 1) ((2)/(3))^(2)`
`= 9 + 8 - (2)/(3) = (49)/(3)` Joule