A nucleus at rest splits into two nuclear parts having same density and radii in ratio 1 : 2 . Their

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13.Nuclei

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A nucleus at rest splits into two nuclear parts having same density and the radii in the ratio $1 : 2$ . Their velocities are in ratio ———

A

$2 : 1$

B

$4 : 1$

C

$6 : 1$

D

$8 : 1$

Solution

$\frac{\mathrm{r}_{1}}{\mathrm{r}_{2}}=\frac{1}{2} \mathrm{so} \frac{\mathrm{m}_{1}}{\mathrm{m}_{2}}=\frac{\frac{4}{3} \pi \mathrm{r}_{1}^{3}}{\frac{4}{3} \pi \mathrm{r}_{2}^{3}} \frac{\rho}{\rho}=\frac{\mathrm{r}_{1}^{3}}{\mathrm{r}_{2}^{3}}=\frac{1}{8}$

$\mathrm{m}_{1}=\mathrm{m}_{0}, \quad \mathrm{m}_{2}=8 \mathrm{m}_{0}$

as $\mathrm{M} \times 0=\mathrm{m}_{1} \mathrm{v}_{1}+\mathrm{m}_{2} \mathrm{v}_{2}$

$\mathrm{m}_{1} \mathrm{v}_{1}=-\mathrm{m}_{2} \mathrm{v}_{2}$

$\left|\frac{v_{1}}{v_{2}}\right|=\frac{m_{2}}{m_{1}}=\frac{8}{1}$

Standard 12

Physics

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