A) 1: 3: 5
B) 5: 3: 1
C) 1: 25: 125
D) 125: 15: 1
Correct Answer: D
Solution :
[d] \[R=\frac{\rho l}{\pi {{r}^{2}}}.\]But \[m=\pi {{r}^{2}}\,ld\] \[\therefore \]\[\pi {{r}^{2}}=\frac{m}{ld}\] \[\therefore \]\[R=\frac{\rho {{l}^{2}}d}{m},\]\[{{R}_{1}}=\frac{\rho {{l}_{1}}^{2}d}{{{m}_{1}}},\]\[{{R}_{2}}=\frac{\rho {{l}_{2}}^{2}d}{{{m}_{2}}}\] \[{{R}_{3}}=\frac{\rho {{l}_{3}}^{2}d}{{{m}_{3}}}\] \[{{R}_{1}}:{{R}_{2}}:{{R}_{3}}=\frac{{{l}_{1}}^{2}}{{{m}_{1}}}:\frac{{{l}_{2}}^{2}}{{{m}_{2}}}:\frac{{{l}_{3}}^{2}}{{{m}_{3}}}\] \[{{R}_{1}}:{{R}_{2}}:{{R}_{3}}=\frac{25}{1}:\frac{9}{3}:\frac{1}{5}=125:15:1\]
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