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