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JEE Main 2023 (11 Apr, Shift 2) · Nucleus: Composition, Size & Nuclear Force

Nucleus: Composition, Size & Nuclear Force question from JEE Main 2023 (11 Apr, Shift 2)

Q16JEE Main 2023 · 11 APR · SHIFT 2Medium

Nucleus: Composition, Size & Nuclear Force

A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is $1 : 2^{1/3}$ . Their respective speeds have a ratio of $n : 1$ . The value of $n$ is __________.

Numerical answer type. Work it out, then open the answer.

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Answer: 2

$R \propto A^{1/3}$ : $\dfrac{R_1}{R_2} = \dfrac{1}{2^{1/3}} \Rightarrow \dfrac{A_1}{A_2} = \dfrac{1}{2}$
Momentum conservation: $\dfrac{v_1}{v_2} = \dfrac{A_2}{A_1} = \dfrac{2}{1}$
So $n = 2$

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