[" Two balls,having linear momenta "bar(p)_(1)=phat i" and "bar(p)_(2)=-phat i," undergo a collision in free space.There "],[" is no external force acting on the balls.Let "vec p_(1)" and "vec p_(2)" be their final momenta.The following "],[" option(s) is (are) NOT ALLOWED for any non-zero value of "p,a_(1),a_(2),b_(1),b_(2),c_(1)" and "c_(2)" ."]

Two balls , having linear momenta vec(p)_(1) = p hat(i) and vec(p)_(2) = - p hat(i) , undergo a collision in free space. There is no external force acting on the balls. Let vec(p)_(1) and vec(p)_(2) , be their final momenta. The following option(s) is (are) NOT ALLOWED for any non -zero value of p , a_(1) , a_(2) , b_(1) , b_(2) , c_(1) and c_(2) (i) vec(p)_(1) = a_(1) hat(i) + b_(1) hat(j) + c_(1) hat(k) , vec(p)_(2) = a_(2) hat(i) + b_(2) hat(j) (ii) vec(p)_(1) = c_(1) vec(k) , vec(p)_(2) = c_(2) hat(k) (iii) vec(p)_(1) = a_(1) hat(i) + b_(1) hat(j) + c_(1) hat(k) ,vec(p)_(2) = a_(2) hat(i) + b_(2) hat(j) - c_(1) hat(k) (iv) vec(p)_(1) = a_(1) hat(i) + b_(1) hat(j) , vec(p)_(2) = a_(2) hat(i) + b_(1) hat(j)

Two balls , having linear momenta vec(p)_(1) = p hat(i) and vec(p)_(2) = - p hat(i) , undergo a collision in free space. There is no external force acting on the balls. Let vec(p)_(1) and vec(p)_(2) , be their final momenta. The following option(s) is (are) NOT ALLOWED for any non -zero value of p , a_(1) , a_(2) , b_(1) , b_(2) , c_(1) and c_(2) (i) vec(p)_(1) = a_(1) hat(i) + b_(1) hat(j) + c_(1) hat(k) , vec(p)_(2) = a_(2) hat(i) + b_(2) hat(j) (ii) vec(p)_(1) = c_(1) vec(k) , vec(p)_(2) = c_(2) hat(k) (iii) vec(p)_(1) = a_(1) hat(i) + b_(1) hat(j) + c_(1) hat(k) ,vec(p)_(2) = a_(2) hat(i) + b_(2) hat(j) - c_(1) hat(k) (iv) vec(p)_(1) = a_(1) hat(i) + b_(1) hat(j) , vec(p)_(2) = a_(2) hat(i) + b_(1) hat(j)

Two balls having linear momenta vecp_(1)=phati and vecp_(2)=-phati, undergo a collision in free space. There is no external force acting on the ball. Let vecp_(1)^(') and vecp_(2)^(') be their final momenta. 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).

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).

The balls, having linear momenta vecp_1=vecpi and vecp_2_2=-vecpi , undergo a collision in free space. There is no external force acting on the balls. Let vecp'_1 and vec p'_2 be their final momenta.The following option (s) is (are) NOT ALLOWED for any non-zero value of p, a_1, a_2, b_1, b_2, c_1 and c_2 .

Two bodies with masses 1 kg and 2 kg have equal kinetic energies. If p_(1) and P_(2) are their repective momenta, then p_(1)//P_(2) is equal to :

If vec(a_(1)) and vec(a_(2)) are two non-collinear unit vectors and if |vec(a_(1)) + vec(a_(2))|=sqrt(3) , then the value of (vec(a_(1))-vec(a_(2))). (2 vec(a_(1))+vec(a_(2))) is :

If vec(a_(1)) and vec(a_(2)) are two non-collinear unit vectors and if |vec(a_(1)) + vec(a_(2))|=sqrt(3) , then the value of (vec(a_(1))-vec(a_(2))). (2 vec(a_(1))+vec(a_(2))) is :

Two bodies with masses m1 kg and m2 kg have equal kinetic energies. If p_(1) and P_(2) are their respective momenta, then p_(1)//P_(2) is equal to :

If vec A_(1) and vec A_(2) are two non-collinear unit vectors and if |vec A_(1)+vec A_(2)|=sqrt(3) then the value of (vec A_(1)-vec A_(2))*(2vec A_(1)+vec A_(2)) is