Two bodies of mass $$4$$ g and $$25$$ g are moving with equal kinetic energies. The ratio of magnitude of their linear momentum is :

The relationship between kinetic energy and momentum is:

$$KE = \frac{p^2}{2m}$$, so $$p = \sqrt{2mKE}$$.

Since both bodies have equal kinetic energy:

$$\frac{p_1}{p_2} = \frac{\sqrt{2m_1 KE}}{\sqrt{2m_2 KE}} = \sqrt{\frac{m_1}{m_2}} = \sqrt{\frac{4}{25}} = \frac{2}{5}$$

The ratio of magnitudes of their linear momenta is $$2 : 5$$, which corresponds to Option (3).

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