Two bodies are having kinetic energies in the ratio 16 : 9 . If they have same linear momentum, the ratio of their masses respectively is:

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TestHub · Accepted Answer

The kinetic energy and the momentum of a moving object are related by
$K = \frac{p^{2}}{2 m} . . . (1)$
Hence, the ratio of the kinetic energies of two objects having masses $m$ and $m'$ can be calculated as follows:
$\begin{array}{rcl} \frac{K}{K^{'}} & = & \frac{\frac{p^{2}}{2 m}}{\frac{p^{2}}{2 m'}} \\ = & \frac{m'}{m} . . . (2) \end{array}$
Substitute the ratio of the kinetic energies into equation (2) and simplify to obtain the ratio of their masses.
$\begin{array}{rcl} \Rightarrow & \frac{16}{9} = \frac{m'}{m} \\ \Rightarrow & m : m' = 9 : 16 \end{array}$

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