JEE Main · 2023 · 25 Jan 2023 · Shift 2 · Modern Physics

A nucleus disintegrates into two smaller parts, which have their velocities in the ratio

3 : 2

. The ratio of their nuclear sizes will be

(\frac{x}{3})^{\frac{1}{3}}

. The value of 'x' is:

Answer: 2

Solution

The parent is at rest, so the fragments carry equal and opposite momenta,

m_{1} v_{1} = m_{2} v_{2}

, giving

\frac{m _{1}}{m _{2}} = \frac{v _{2}}{v _{1}} = \frac{2}{3}

. Nuclear matter has a fixed density, so mass goes as the cube of the radius and

(\frac{r _{1}}{r _{2}})^{3} = \frac{m _{1}}{m _{2}} = \frac{2}{3}

. Hence

\frac{r _{1}}{r _{2}} = (\frac{2}{3})^{1/3}

, and comparison with

(\frac{x}{3})^{1/3}

gives

x = 2

JEE Main · 2023 · 25 Jan 2023 · Shift 2 · Integer answer

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