[" Two balls,having linear momenta "vec p_(1)=pi" and "vec 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 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).

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)

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 .

If vec a_(1) and vec a_(2) are two non collinear unit vectors inclined at 60^(0) to each other than the value of (vec a_(1)-vec a_(2))*(2vec a_(1)+vec a_(2)) is

Two point dipoles of dipole moment vec(p)_(1) and vec(p)_(2) are at a distance x from each other and vec(p)_(1)||vec(p)_(2) . The force between the dipoles 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))*(2vec A_(1)+vec A_(2)) is

Two electric dipole vec(P_1) and vec(P_2) are kept as shown in figure. Net electric field at point S is E makes an angle 37^0 with vec(P_1) then find ratio of vec(P_1) and vec(P_2)