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

A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of $2: 1$. After disintegration they will move :
  1. in the same direction with same speed.
  2. in opposite directions with the same speed.
  3. in opposite directions with speed in the ratio of $2: 1$ respectively.
  4. in opposite directions with speed in the ratio of $1: 2$ respectively.

Solution

By conservation of momentum $\begin{aligned}& \mathrm{p}_{\mathrm{i}}=\mathrm{p}_{\mathrm{f}} \\ & \mathrm{O}=\mathrm{m}_1 \mathrm{u}_{1+} \mathrm{m}_2 \mathrm{u}_2 \\& \frac{\mathrm{u}_1}{\mathrm{u}_2}=-\left[\frac{1}{2}\right] \text { as } \frac{\mathrm{m}_1}{\mathrm{~m}_2}=\frac{2}{1} \end{aligned}$ move in opposite direction with speed ratio $1: 2$

Asked in: JEE Main 2024 (09 Apr Shift 2)

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