A) 1 : 3 : 5
B) 5 : 3 : 1
C) 1 : 25 : 125
D) 125 : 45 : 3
Correct Answer: D
Solution :
[d] \[R=\frac{\rho l}{\pi {{r}^{2}}}.\]But \[m=\pi {{r}^{2}}ld\text{ }\therefore \pi {{r}^{2}}=\frac{m}{ld}\] \[\therefore {{R}_{1}}=\frac{pl_{1}^{2}d}{{{m}_{1}}},{{R}_{2}}=\frac{pl_{2}^{2}d}{{{m}_{2}}};{{R}_{3}}=\frac{pl_{3}^{2}d}{{{m}_{3}}}\] \[{{R}_{1}}:{{R}_{2}}:{{R}_{3}}=\frac{l_{1}^{2}}{{{m}_{1}}}:\frac{l_{2}^{2}}{{{m}_{2}}}:\frac{l_{3}^{2}}{{{m}_{3}}}=125:45:3\]
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