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13.Nuclei
medium
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
$2:1$
Solution
(a) By conservation of momentum $m_1v_1 = m_2v_2$
==> $\frac{{{v_1}}}{{{v_2}}} = \frac{8}{1} = \frac{{{m_2}}}{{{m_1}}}$…… $(i) $
Also from $r \propto {A^{1/3}}$
==> $\frac{{{r_1}}}{{{r_2}}} = {\left( {\frac{{{A_1}}}{{{A_2}}}} \right)^{1/3}} = {\left( {\frac{1}{8}} \right)^{1/3}} = \frac{1}{2}$.
Standard 12
Physics
