A) \[8:27\]
B) \[2:3\]
C) \[3:2\]
D) \[4:9\]
Correct Answer: C
Solution :
\[\frac{{{V}_{1}}}{{{V}_{2}}}=\frac{8}{27}\] \[{{m}_{1}}{{V}_{1}}={{m}_{2}}{{V}_{2}}\] \[\frac{{{m}_{1}}}{{{m}_{2}}}=\frac{{{V}_{2}}}{{{V}_{1}}}=\frac{27}{8}\] \[\frac{\rho \times \frac{4}{3}\pi R_{1}^{3}}{\rho \times \frac{4}{3}\pi R_{2}^{3}}\] \[\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)={{\left( \frac{27}{8} \right)}^{\frac{1}{3}}}\] \[={{\left( \frac{3}{2} \right)}^{3\times \frac{1}{3}}}\] \[\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{3}{2}\]
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