JEE Main · 2023 · 11 Apr 2023 · Shift 2 · Conservation of Momentum

A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is

1 : 2^{1/3}

. Their respective speed have a ratio of

n : 1

. The value of n is

____

Answer: 2

Solution

By conservation of momentum:

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

, so

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

. The nuclear radius is proportional to

A^{1/3}

where

A

is the mass number. Given the size ratio is

1 : 2^{1/3}

, the mass number ratio is

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

. Therefore,

\frac{v _{1}}{v _{2}} = \frac{A _{2}}{A _{1}} = \frac{2}{1}

, giving

n = 2

JEE Main · 2023 · 11 Apr 2023 · Shift 2 · Integer answer

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