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Q.
A nucleus disintegrates into two nuclear parts which have their velocities in the ratio $2:1$ . The ratio of their nuclear size will be
NTA AbhyasNTA Abhyas 2020Nuclei
Solution:
According to the law of conservation of momentum, we get
$m_{1}v_{1}=m_{2}v_{2}$
Or $\left(\frac{m_{1}}{m_{2}}\right)=\left(\frac{v_{2}}{v_{1}}\right)$
But $m=\frac{4}{3}\pi r^{3} \, \rho \, \, or \, \, m \, \propto r^{3}$
$\Rightarrow \, \, \frac{m_{1}}{m_{2}}=\frac{r_{1}^{2}}{r_{2}^{3}}$
$\therefore \, \, \frac{r_{1}^{3}}{r_{2}^{3}}=\frac{v_{2}}{v_{1}}=\frac{1}{2}$
$\Rightarrow \, \frac{r_{1}}{r_{2}}=\left(\frac{1}{2}\right)^{\frac{1}{3}}$
$\therefore \, \, r_{1}:r_{2}=1:\left(2\right)^{\frac{1}{3}}$