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Two balls having linear momenta vecp(1)=...

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).`

A

`vecp_(1)^(')=a_(1)hati+b_(1)hatj+c_(1)hatk, vecp_(2)^(')=a_(2)hati+b_(2)hatj`

B

`vecp_(1)^(')=c_(1)hatk, vecp_(2)^(')+c_(2)hatk`

C

`vecp_(1)^(')=a_(1)hati+b_(1)hatj+c_(1)hatk, vecp_(2)^(')=a_(2)hatib_(2)hatj-c_(2)hatk`

D

`vecp_(1)^(')=a_(1)hati+b_(1)hatj, vecp_(2)^(')=a_(2)hati+b_(1)hatj`

Text Solution

Verified by Experts

The correct Answer is:
A, D
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)^(')+p_(2)^(')` will be zero. Similarly we can check other options. Hence correct options a and d.
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