Two bodies are having kinetic energies in the ratio 16: 9 . If they...

The kinetic energy and the momentum of a moving object are related by

$K = \dfrac{{p}^{2}}{2m} . . . \left(1\right)$

Hence, the ratio of the kinetic energies of two objects having masses $m$ and $m '$ can be calculated as follows:

$\begin{cases}\dfrac{K}{{K}^{'}} & = & \dfrac{\dfrac{{p}^{2}}{2m}}{\dfrac{{p}^{2}}{2m '}} \\ & = & \dfrac{m '}{m} . . . \left(2\right)\end{cases}$

Substitute the ratio of the kinetic energies into equation (2) and simplify to obtain the ratio of their masses.

$\begin{cases} & ⇒ & \dfrac{16}{9} = \dfrac{m '}{m} \\ & ⇒ & m: m ' = 9: 16\end{cases}$