Question

Two balls, having linear moments ${\overrightarrow{p}}_1=p\hat{i}$ and ${\overrightarrow{p}}_2=-p\hat{i}$, undergo a collision in free space. There is no external force acting on the balls. Let ${\overrightarrow{p}}_1$ and $\overrightarrow{P_2}$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. ${\overrightarrow{p}}_1=a_1\hat{i}+b_1\hat{j}+c_1\hat{k}$
  ${\overrightarrow{p}}_2=a_2\hat{i}+b_2\hat{j}$
• B. ${\overrightarrow{p}}_1=c_1\hat{k}$
  ${\overrightarrow{p}}_2=c_2\hat{k}$
• C. ${\overrightarrow{p}}_1=a_1\hat{i}+b_1\hat{j}+c_1\hat{k}$
  ${\overrightarrow{p}}_2=a_2\hat{i}+b_2\hat{j}-c_1\hat{k}$
• D. ${\overrightarrow{p}}_1=a_1\hat{i}+b_1\hat{j}$
  ${\overrightarrow{p}}_2=a_2\hat{i}+b_1\hat{j}$

Answer 1

Answer: (A), (D)

The correct options are
A ${\overrightarrow{p}}_1=a_1\hat{i}+b_1\hat{j}+c_1\hat{k}$
${\overrightarrow{p}}_2=a_2\hat{i}+b_2\hat{j}$
D ${\overrightarrow{p}}_1=a_1\hat{i}+b_1\hat{j}$

${\overrightarrow{p}}_2=a_2\hat{i}+b_1\hat{j}$