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  • A heavy nucleus at rest breaks into two fragments which fly off with velocities in the ratio 3 : 1. The ratio of radii of the fragments is:Option: 1</stro

A heavy nucleus at rest breaks into two fragments which fly off with velocities in the ratio 3 : 1. The ratio of
radii of the fragments is:

Option: 1

1: 3^{1 / 3}


Option: 2

3^{1 / 3}: 4


Option: 3

4: 1


Option: 4

2: 1


Answers (1)

best_answer

As the heavy nucleus at rest breaks, therefore according to law of conservation of momentum, we get

\mathrm{m}_1 \mathrm{v}_1+\mathrm{m}_2 \mathrm{v}_2=0 \quad \text { or } \quad \frac{\mathrm{v}_1}{\mathrm{v}_2}=\frac{\mathrm{m}_2}{\mathrm{~m}_1}=\frac{3}{1}                         (i)

As nuclear density is same,

\therefore \frac{\mathrm{m}_1}{\mathrm{~m}_2}=\frac{\rho \frac{4}{3} \pi \mathrm{R}_1^3}{\rho \frac{4}{3} \pi \mathrm{R}_2^2}=\frac{\mathrm{R}_1^3}{\mathrm{R}_2^3} \quad \text { or } \quad \frac{\mathrm{R}_1^3}{\mathrm{R}_2^3}=\frac{\mathrm{m}_1}{\mathrm{~m}_2}=\frac{1}{3}            \text { (Using (i)) } 

\therefore R_1: R_2=1: 3^{1 / 3}

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