Question

Two balls, having linear momenta $\rho_1 = p \widehat{i}$ and $\rho_2 = - p \widehat{i},$ undergo a collision in free space. There is no external force acting on the balls. Let $\rho_2 ' \, and \, \rho_2 '$. be their final momenta. The following option figure (s) is (are) not allowed for any non-zero value of $\rho, a_1, a_2, b_1, b_2, c_1 \, and c_2$.

• A. $\rho_1' = a_1 \widehat{ i } + b_1 \widehat{ j} + c_1 \widehat{k}, \rho_2 = a_2 \widehat{ i } + b_2 \widehat{ j}$
• B. $\rho_1 ' = c_1 \widehat{ k} , \rho_2 = c_2 \widehat{ k}$
• C. $\rho_1' = a_1 \widehat{ a_1 } \widehat{ i} + b_1 \widehat{ j } + c_1 \widehat{k} , \rho_2 = a_2 \widehat{ i } + b_2 \widehat{ j} - c_1 \widehat{ k}$
• D. $\rho_1 ' = a_1 \widehat{i} + b_1 \widehat{j} + c_1 \widehat{k}, \rho_2 = a_2 \widehat{i} + b_1 \widehat{j}$

Answer 1

Answer: (D)

$\rho_1 ' = a_1 \widehat{i} + b_1 \widehat{j} + c_1 \widehat{k}, \rho_2 = a_2 \widehat{i} + b_1 \widehat{j}$

Answer 2

Initial momentum of the system $\rho_1 + \rho_2 = 0$
$\therefore$ Final momentum $\rho_1 ' + \rho_2 '$ should also be zero
Option (b) is allowed because if we put $c_1 = - c_2 \ne 0,$
$\rho_1 ' + \rho_2 '$ W'H t>e zero. Similary, we can check other options.
$\therefore$ Correct options are (a) and (d).