Question
If the kinetic energy of a light and heavy body is equal, then whose momentum is less?
✓
Answer
Let
$\begin{aligned} m _1 & > m _2 \\ \frac{1}{2} m_1 v _1^2 & =\frac{1}{2} m_2 v _2^2 \\ \frac{m_1}{m_2} & =\left(\frac{ v _2}{ v _1}\right)^2\end{aligned}$
Hence, $\quad\left( m _1 v_1\right) v _1=\left( m _2 v_2\right) v_2$
$\begin{aligned} m _1 & > m _2 \\ \frac{1}{2} m_1 v _1^2 & =\frac{1}{2} m_2 v _2^2 \\ \frac{m_1}{m_2} & =\left(\frac{ v _2}{ v _1}\right)^2\end{aligned}$
Hence, $\quad\left( m _1 v_1\right) v _1=\left( m _2 v_2\right) v_2$
Hence, $\quad P _1 v _1= P _2 v _2$
But,
$\frac{v_2}{v_1}=\sqrt{\frac{m_1}{m_2}}=\frac{P_1}{P_2}$
But, $m_1>m_2$ so $v _2> v _1$
Hence,$P_1>P_2$
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