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Two bodies are having kinetic energies in the ratio $$16 : 9$$. If they have same linear momentum, the ratio of their masses respectively is:
Kinetic energy in terms of momentum: $$K = \frac{p^2}{2m}$$
Since both bodies have the same linear momentum $$p$$:
$$K_1 = \frac{p^2}{2m_1}$$ and $$K_2 = \frac{p^2}{2m_2}$$
Taking the ratio:
$$\frac{K_1}{K_2} = \frac{m_2}{m_1}$$
Given $$\frac{K_1}{K_2} = \frac{16}{9}$$:
$$\frac{m_2}{m_1} = \frac{16}{9}$$
$$\frac{m_1}{m_2} = \frac{9}{16}$$
The ratio of their masses is $$\mathbf{9 : 16}$$.
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