A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of $$2 : 1$$. After disintegration they will move :

By conservation of momentum: $$\vec{p}_1 + \vec{p}_2 = 0$$ (nucleus initially at rest).

So $$m_1v_1 = m_2v_2$$, and they move in opposite directions.

$$\frac{v_1}{v_2} = \frac{m_2}{m_1} = \frac{1}{2}$$.

The heavier nucleus (mass ratio 2) moves slower, and the lighter one (mass ratio 1) moves faster, in opposite directions with speeds in ratio 1:2.

The correct answer is Option 4: in opposite directions with speed in the ratio of 1:2 respectively.