A heavy nucleus at rest breaks into two fragments which fly off with velocities in the ratio 8: 1. The ratio of radii of the fragments is

Question

A heavy nucleus at rest breaks into two fragments which fly off with velocities in the ratio 8: 1. The ratio of radii of the fragments is (A) 1: 2 (B) 1: 4 (C) 4: 1 (D) 2: 1

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/f27598a2bae6ce8b884a5b4a65ef4e9c-.png" /> By conservation of momentum m1 v1=m2 v2 ⇒ (v1/v2)=(8/1)=(m2/m1) ...(i) Also from r propto A1 / 3 ⇒ (r1/r2)=((A1/A2))1 / 3=((1/8))1 / 3=(1/2).

Q. A heavy nucleus at rest breaks into two fragments which fly off with velocities in the ratio $8 : 1.$ The ratio of radii of the fragments is

1 : 2

1 : 4

4 : 1

2 : 1

By conservation of momentum $m_{1} v_{1} = m_{2} v_{2}$
$\Rightarrow \frac{v _{1}}{v _{2}} = \frac{8}{1} = \frac{m _{2}}{m _{1}} ... (i)$
Also from $r \propto A^{1/3}$
$\Rightarrow \frac{r _{1}}{r _{2}} = (\frac{A _{1}}{A _{2}})^{1/3} = (\frac{1}{8})^{1/3} = \frac{1}{2}$ .

Q. A heavy nucleus at rest breaks into two fragments which fly off with velocities in the ratio 8:1. The ratio of radii of the fragments is