Two balls of masses \( m_{1} \) and \( m_{2} \) are moving towards each other with speeds \( u_{...

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Two balls of masses \( m_{1} \) and \( m_{2} \) are moving towards each other with speeds \( u_{1} \) and \( u_{2} \), respectively. They collide head-on and their speeds are \( v_{1} \) and \( v_{2} \) after collision
\( \mathrm{P} \) \( \left(m_{1}=8 \mathrm{~kg}, m_{2}=2 \mathrm{~kg}, u_{2}=3 \mathrm{~m} / \mathrm{s}\right) \).

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\begin{tabular}{|l|l|}
\hline \multicolumn{1}{|c|}{ Column I } & Column II \\
\hline i. \( \begin{array}{l}\text { The speed } u_{1} \text { (in } \mathrm{m} / \mathrm{s} \text { ) so that both } \\
\text { balls move in same direction if } \\
\text { coefficient of restitution is } e=0.5\end{array} \) & a. \( \frac{1}{14} \) \\
\hline ii. The speed \( u_{1} \) (in \( \mathrm{m} / \mathrm{s} \) ) so that the \\
maximum fraction of energy is \\
transformed to \( m_{2} \) (assume elastic & \\
collision)
\end{tabular}
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