Two bodies of masses $m_{1}$ and $m_{2} (> m_{1})$ have equal linear momentum. Which body possesses greater kinetic energy?

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Solution

Step 1: Given data
Two bodies $m_{1}$ and $m_{2}$ have equal linear momentum and $m_{2} > m_{1}$ +
Step 2: Comparing Kinetic energy for $m_{1}$ and $m_{2}$
$K . E = \frac{p^{2}}{2 m}$ where p is momentum and m is mass
For the given masses $m_{1}$ and $m_{2}$ ,
$K . E_{1} = \frac{p^{2}}{2 m_{1}}$ ……..1
$K . E_{2} = \frac{p^{2}}{2 m_{2}}$ ………..2
Dividing 1 and 2,
$\frac{K . E_{1}}{{K . E}_{2}} = \frac{(\frac{p^{2}}{2 m_{1}})}{(\frac{p^{2}}{2 m_{2}})}$
$\frac{K . E_{1}}{{K . E}_{2}} = \frac{m_{2}}{m_{1}}$
From the above, we can conclude that $K . E_{1}$ is directly proportional to $m_{2}$ .
Since $m_{2} > m_{1}$ , it is clear that $K . E_{1}$ will be higher than $K . E_{2}$ .
Hence, $m_{1}$ will possess greater Kinetic energy than $m_{2}$ .

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