\( A \) and \( B \) are two particles, initially they are moving with velocity \( v_{1} \) and \....

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\( A \) and \( B \) are two particles, initially they are moving
\( \mathrm{P} \)
with velocity \( v_{1} \) and \( v_{2} \). Their masses are \( m_{1} \) and \( m_{2} \). Their accelerations are \( a_{1} \) and \( a_{2} \) respectively. ' \( F \) ' denotes force and ' \( P \) ' denotes momentum.
\begin{tabular}{|l|l|l|l|}
\hline & \multicolumn{1}{|c|}{ Column I } & & Column II \\
\hline (A) & \begin{tabular}{l}
If \( F_{\mathrm{COM}}=0 \) \\
{\( [\mathrm{COM} \) denotes } \\
centre of mass \( ] \)
\end{tabular} & (p) & \( \frac{m_{1} a_{1}+m_{2} a_{2}}{m_{1}+m_{2}} \) \\
\hline (B) & \( a_{\mathrm{COM}} \) & (q) & \( \frac{m_{1} v_{1}+m_{2} v_{2}}{m_{1}+m_{2}} \) \\
\hline (C) & \( V_{\mathrm{COM}} \) & (r) & \( P_{\mathrm{COM}}= \) constant \\
\hline
\end{tabular}
(1) \( \mathrm{A} \rightarrow \mathrm{p}, \mathrm{B} \rightarrow \mathrm{r}, \mathrm{C} \rightarrow \mathrm{q} \)
(2) \( \mathrm{A} \rightarrow \mathrm{r}, \mathrm{B} \rightarrow \mathrm{p}, \mathrm{C} \rightarrow \mathrm{q} \)
(3) \( \mathrm{A} \rightarrow \mathrm{q}, \mathrm{B} \rightarrow \mathrm{r}, \mathrm{C} \rightarrow \mathrm{p} \)
(4) \( \mathrm{A} \rightarrow \mathrm{p}, \mathrm{B} \rightarrow \mathrm{q}, \mathrm{C} \rightarrow \mathrm{r} \)


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