A nucleus disintegrates into two nuclear parts which have their velocities in the ratio 2 : 1 . The ratio of their nuclear sizes will be: - Physics MCQ AIEEE 2004 2026 | ExamTest.live

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A nucleus disintegrates into two nuclear parts which have their velocities in the ratio 2 : 1 . The ratio of their nuclear sizes will be:

Solution & Step-by-step Explanation

From the conservation of linear momentum: m_{1} v_{1} = m_{2} v_{2} ⟹ \frac{m _{1}}{m _{2}} = \frac{v _{2}}{v _{1}} Given \frac{v _{1}}{v _{2}} = \frac{2}{1} ⟹ \frac{m _{1}}{m _{2}} = \frac{1}{2} .Since mass is proportional to volume and V \propto R^{3} : \frac{m _{1}}{m _{2}} = (\frac{R _{1}}{R _{2}})^{3} \frac{1}{2} = (\frac{R _{1}}{R _{2}})^{3} ⟹ \frac{R _{1}}{R _{2}} = (\frac{1}{2})^{1/3} Ratio of nuclear sizes is 1 : 2^{1/3} .

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A nucleus disintegrates into two nuclear parts which have their velocities in the ratio 2 : 1 . The ratio of their nuclear sizes will be:

2^{1/3} : 1

1 : 2^{1/3}

3^{1/2} : 1

1 : 2^{1/3}

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