A point mass of 1kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1kg mass reverses its direction and moves with a speed of `2ms^-1`. Which of the following statements (s) is (are) correct for the system of these two masses?

Options

A. `(i) ,(ii)`
B. `(ii) ,(iii)`
C. `(i) ,(iv)`
D. `(i),(iii)`

Answer

D

Explanation

By the momentum conservation
`1 xx u = - 1 xx 2 + 5 v_(2)` (i)
`-2 + u = v_(2)` (ii)
Solving , `u = 3 m//s , v_(2) = 1 m//s`
The momentum of system `= 1 xx = 3 kg m//s`, (i) is `O.K`. Momentum of `5 kg` after collision `= 5 v_(2) = 5 kg m//s`, (ii) is wrong.
`v_(c.m.) = (1 xx u + 5 xx 0 )/(1 + 5) = (u)/(6) = (3)/(6) = (1)/(2) m//s`
`(K.E.)_(c.m.) = (1)/(2) (1 + 5) v_(c.m.)^(2) = 3((1)/(2))^(2) = 0.75 J`
(iii) is `O.K`.
Total `K.E.` of the system `= (1)/(2) xx 1 xx u^(2) = ((3)^(2))/(2) = 4.5 J`
(iv) is wrong.