A body of mass $$8 \text{ kg}$$ and another of mass $$2 \text{ kg}$$ are moving with equal kinetic energy. The ratio of their respective momenta will be

Two bodies of masses $$8 \text{ kg}$$ and $$2 \text{kg}$$ have equal kinetic energy and we need to find the ratio of their momenta.

Kinetic energy can be expressed in terms of momentum as $$KE = \dfrac{p^2}{2m}$$. Rearranging gives $$p = \sqrt{2m \cdot KE}$$.

Since $$KE_1 = KE_2 = KE$$, substituting yields $$p_1 = \sqrt{2 \times 8 \times KE} = \sqrt{16 \cdot KE}$$ and $$p_2 = \sqrt{2 \times 2 \times KE} = \sqrt{4 \cdot KE}$$.

From this, $$\dfrac{p_1}{p_2} = \dfrac{\sqrt{16 \cdot KE}}{\sqrt{4 \cdot KE}} = \sqrt{\dfrac{16}{4}} = \sqrt{4} = 2$$ so that $$p_1 : p_2 = 2 : 1$$.

The correct answer is Option B: $$2:1$$.