Two balls having linear momenta `vecp_(1)=phati` and `vecp_(2)=-phati, ` undergo a collision in fre space. There is no external force acting on the ball. Let `vecp_(1)^(')` and `vecp_(2)^(')` be their final moment. Which of the following option(s) is (are) NOT ALLOWED for an non zero value of `p,a_(1),a_(2),b_(1),b_(2), c_(1)` and `c_(2).`

Options

A. `vecP_(1)^(') = a_1hati + b_1 hatj + a_1k, vecp_2^' = a_2hati + b_2hatj`
B. `vecP_(1)^(') = c_1k, vecp_2^' = c_2k`
C. `vecP_(1)^(') = a_1hati + b_1 hatj + a_1k, vecp_2^' = a_2hati + b_2hatj - c_2k`
D. `vecP_(1)^(') = a_1hati + b_1 hatj ,vecp_2^' = a_2hati + b_2hatj`

Answer

A, D

Explanation

Initial momentum of the system. , `" " vecp_1 + vecp_2 = 0`
Therefore, final momentum `vecp_1^' + vecp_2^'` should also be zero.
Option (b) is allowed because if we put ` C_1 = - C_2 != 0, vecp_1^' vecp_2^'` will be zero. Similarly, we can check other options. Hence correct options are (a) and (d).