Question

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

4: 1
8: 1
2:1
6: 1

Answer 1

I think this is the answer

Answer 2

Answer:

8 : 1

Explanation:

As per the question,

A nucleus at rest splits into two nuclear parts having radii in the ratio 1:2.

let the first radius be R

And the second radius be r

∴ $\frac{r}{R}=\frac{1}{2}$

According to conservation of momentum

MV = mv

$\frac{V}{v}=\frac{m}{M}$

And also density is given by

$\rho=\frac{mass}{volume}=\frac{M}{\frac{4}{3}\pi R^{3}}\\\Rightarrow M=\frac{4}{3}\pi R^{3}\rho$

That is,

$M\alpha R^{3}$

$\Rightarrow \frac{M}{m}=\frac{R^{3}}{r^{3}}$

Or

$\Rightarrow \frac{v}{V}=\frac{R^{3}}{r^{3}}$

$\Rightarrow \frac{M}{m}=(\frac{2}{1})^{3}$

$\Rightarrow \frac{M}{m}=\frac{8}{1}$

Hence, the ratio of their velocities are 8:1