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# Two bodies of equal masses move with the uniform velocities $v$ and $3v$ respectively. Find the ratio of their kinetic energies.

As given, Two bodies of equal masses move with the uniform velocities $v$ and $3v$ respectively. Let $m$ be the mass of the two bodies.

Therefore, kinetic energy of the body with $v$ velocity $K_1=\frac{1}{2}mv^2$

And kinetic energy of the body with $3v$ velocity $K_2=\frac{1}{2}m( 3v)^2$

Therefore, ratio between the kinetic energies $=\frac{K_1}{K_2}$

Or $\frac{K_1}{K_2}=\frac{\frac{1}{2}mv^2}{\frac{1}{2}m( 3v)^2}$

Or $\frac{K_1}{K_2}=\frac{v^2}{9v^2}$

Or $\frac{K_1}{K_2}=\frac{1}{9}$

Or $K_1:K_2=1:9$

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