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(A) The kinetic energy $(K.E.)$ of a particle with mass $m$ and momentum $p$ is given by the formula: $K.E. = \frac{p^2}{2m}$.Given that both particle

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$5:1$

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(A) The kinetic energy $(K.E.)$ of a particle with mass $m$ and momentum $p$ is given by the formula: $K.E. = \frac{p^2}{2m}$.Given that both particles have the same momentum $(p_1 = p_2 = p)$,the ratio of their kinetic energies is:$\frac{K.E._1}{K.E._2} = \frac{p^2 / (2m_1)}{p^2 / (2m_2)} = \frac{m_2}{m_1}$.Substituting the given masses $m_1 = 1\,kg$ and $m_2 = 5\,kg$:$\frac{K.E._1}{K.E._2} = \frac{5}{1} = 5:1$.

$2$ particles of mass $1\,kg$ and $5\,kg$ have the same momentum. Calculate the ratio of their kinetic energies $(K.E.)$.

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