question_answer

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                                                      [EAMCET (Engg.) 2001]

A)            1 : 2

B)            1 : 4

C)            4 : 1                                          

D)            2 : 1

Correct Answer: A

Solution :

                      By conservation of momentum m1v1 = m2v2 Þ  \[\frac{{{v}_{1}}}{{{v}_{2}}}=\frac{8}{1}=\frac{{{m}_{2}}}{{{m}_{1}}}\]                              ?? (i) Also from \[r\propto {{A}^{1/3}}\]  Þ \[\frac{{{r}_{1}}}{{{r}_{2}}}={{\left( \frac{{{A}_{1}}}{{{A}_{2}}} \right)}^{1/3}}={{\left( \frac{1}{8} \right)}^{1/3}}=\frac{1}{2}\].