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Solve the following :

Question:

Find the ratio of the linear momenta of two particles of masses $1.0 \mathrm{Kg}$ and $4.0 \mathrm{Kg}$ if their kinetic energies are equal.

Solution:

$\frac{1}{2} m_{1} v_{1}^{2}=\frac{1}{2} m_{2} v_{2}^{2} \Rightarrow \frac{v_{2}}{v_{1}}=\sqrt{\frac{m_{1}}{m_{2}}}=\sqrt{\frac{1}{4}}=\frac{1}{2}$

$p_{1} v_{1}=p_{2} v_{2} \Rightarrow \frac{p_{1}}{p_{2}}=\frac{v_{2}}{v_{1}}$

$\Rightarrow \frac{p_{1}}{p_{2}}=\frac{1}{2}$

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