A) \[6:1\]
B) \[2:1\]
C) \[8:1\]
D) \[4:1\]
Correct Answer: C
Solution :
: Let Ai and A2 be the mass numbers of the two nuclear parts. Their radii are given by \[{{R}_{1}}={{R}_{0}}A_{1}^{1/3}\] ?...(i) and \[{{R}_{2}}={{R}_{0}}A_{2}^{1/3}\] ?....(ii) Dividing eqn. (i) by eqn. (ii), we get \[\frac{{{R}_{1}}}{{{R}_{2}}}={{\left( \frac{{{A}_{1}}}{{{A}_{2}}} \right)}^{1/3}}\] or \[\frac{{{A}_{1}}}{{{A}_{2}}}={{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{3}}\] As \[\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{1}{2}\] (given_ \[\therefore \] \[\frac{{{A}_{1}}}{{{A}_{2}}}={{\left( \frac{1}{2} \right)}^{3}}=\frac{1}{8}\] Hence the ratio of their masses is \[\frac{{{m}_{1}}}{{{m}_{2}}}=\frac{1}{8}\] ?..(iii) According to law of conservation of linear Momentum magnitude of \[{{p}_{1}}\] = magnitude of \[{{p}_{2}}\] i.e., \[{{m}_{1}}{{v}_{1}}={{m}_{2}}{{v}_{2}}\] or \[\frac{{{v}_{1}}}{{{v}_{2}}}=\frac{{{m}_{2}}}{{{m}_{1}}}=\frac{8}{1}\] (using (iii))
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