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JEE Advcance 2008
paper 1
Multiple correct answers - Select all that apply
Question
The balls, having linear momenta $\overrightarrow{\mathrm{p}}_1=\mathrm{p} \hat{\mathrm{i}}$ and $\overrightarrow{\mathrm{p}}_2=-\mathrm{p} \hat{\mathrm{i}}$, 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 $\mathrm{p}, \mathrm{a}_1, \mathrm{a}_2, \mathrm{~b}_1, \mathrm{~b}_2, \mathrm{c}_1$ and $\mathrm{c}_2$.
Select ALL correct options:
A
$\quad \begin{aligned} \overrightarrow{\mathrm{p}}_1^{\prime} & =\mathrm{a}_1 \hat{\mathrm{i}}+\mathrm{b}_1 \hat{\mathrm{j}}+\mathrm{c}_1 \hat{\mathrm{k}} \\ \overrightarrow{\mathrm{p}}_2^{\prime} & =\mathrm{a}_2 \hat{\mathrm{i}}+\mathrm{b}_2 \hat{\mathrm{j}}\end{aligned}$
B
$\begin{aligned} & \overrightarrow{\mathrm{p}}_1^{\prime}=\mathrm{c}_1 \hat{\mathrm{k}} \\ & \overrightarrow{\mathrm{p}}_2^{\prime}=\mathrm{c}_2 \hat{\mathrm{k}}\end{aligned}$
C
$\begin{aligned} & \overrightarrow{\mathrm{p}}_1^{\prime}=\mathrm{a}_1 \hat{\mathrm{i}}+\mathrm{b}_1 \hat{\mathrm{j}}+\mathrm{c}_1 \hat{\mathrm{k}} \\ & \overrightarrow{\mathrm{p}}_2^{\prime}=\mathrm{a}_2 \hat{\mathrm{i}}+\mathrm{b}_2 \hat{\mathrm{j}}-\mathrm{c}_1 \hat{\mathrm{k}}\end{aligned}$
D
$\begin{aligned} & \overrightarrow{\mathrm{p}}_1^{\prime}=\mathrm{a}_1 \hat{\mathrm{i}}+\mathrm{b}_1 \hat{\mathrm{j}} \\ & \overrightarrow{\mathrm{p}}_2^{\prime}=\mathrm{a}_2 \hat{\mathrm{i}}+\mathrm{b}_1 \hat{\mathrm{j}}\end{aligned}$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
⚠ Partially correct. Some answers are missing.
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