Question

Select One Option Correct from the following :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, $a_1, a_2, b_1, b_2, c_1 and c_2$.
(A)$\vec{p}^{'}_{1} = a_1 \hat{i}+ b_1 \hat{j}+ c_1 \hat{k},\vec{p}^{'}_{2} = a_2 \hat{i} + b_2 \hat{j}$
(B) $\vec{p}^{'}_{1} =c_1 \hat{k}, \vec{p}^{'}_{2} = c_2 \hat{k}$
(C)$\vec{p}^{'}_{1} = a_1 \hat{i}+ b_1 \hat{j}+ c_1 \hat{k},\vec{p}^{'}_{2} = a_2 \hat{i} + b_2 \hat{j} - c_1\hat{k}$
(D)$\vec{p}^{'}_{1} = a_1 \hat{i}+ b_1 \hat{j},\vec{p}^{'}_{2} = a_2 \hat{i} + b_1 \hat{j}$

Answer 1

Select One Option Correct from the following :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, $a_1, a_2, b_1, b_2, c_1 and c_2$.

(A)$\vec{p}^{'}_{1} = a_1 \hat{i}+ b_1 \hat{j}+ c_1 \hat{k},\vec{p}^{'}_{2} = a_2 \hat{i} + b_2 \hat{j}$

(B) $\vec{p}^{'}_{1} =c_1 \hat{k}, \vec{p}^{'}_{2} = c_2 \hat{k}$

✔️ (C)$\vec{p}^{'}_{1} = a_1 \hat{i}+ b_1 \hat{j}+ c_1 \hat{k},\vec{p}^{'}_{2} = a_2 \hat{i} + b_2 \hat{j} - c_1\hat{k}$

(D)$\vec{p}^{'}_{1} = a_1 \hat{i}+ b_1 \hat{j},\vec{p}^{'}_{2} = a_2 \hat{i} + b_1 \hat{j}$