• question_answer A nucleus disintegrates into two nuclear parts which have their velocities in the ratio 2:1. The ratio of their nuclear sizes will be: A) ${{2}^{\frac{1}{3}}}:1$               B) $1:{{3}^{\frac{1}{2}}}$   C)   ${{3}^{\frac{1}{3}}}:1$   D)   $1:{{2}^{\frac{1}{3}}}$

According to the law of conservation of momentum $\frac{{{m}_{1}}}{{{m}_{2}}}=\frac{{{v}_{2}}}{{{v}_{1}}}=\frac{1}{2}$ Since, masses are directly proportional to volume as densities are roughly same, so it follows that:             $\frac{{{m}_{1}}}{{{m}_{2}}}\propto \frac{r_{1}^{3}}{r_{2}^{3}}$or $\frac{{{r}_{1}}}{{{r}_{2}}}\propto {{\left( \frac{{{m}_{1}}}{{{m}_{2}}} \right)}^{\frac{1}{3}}}$ $\therefore$ratio of nuclear sizes$=\frac{1}{{{2}^{1/3}}}.$ Hence, the correction option is (d).