A) 1 : 1 : 1
B) 1 : 2 : 3
C) 9 : 4 : 1
D) 27 : 6 : 1
Correct Answer: D
Solution :
Resistance (R) of a wire is directly proportional to its length \[(l)\] and inversely proportional to area of cross-section (A) ie, \[R=\rho \frac{l}{A}\] where \[\rho \] is specific resistance. Mass = volume \[\times \] density \[=A\,l\,d\] \[\Rightarrow \] \[A=\frac{m}{ld}\] \[\therefore \] \[R=\rho \frac{l}{m/ld}=\rho \frac{{{l}^{2}}d}{m}\] Given, \[{{m}_{1}}:{{m}_{2}}:=1:2:3\] and \[{{l}_{1}}:{{l}_{2}}:{{l}_{3}}=3:2:1\] \[\therefore \] \[{{R}_{1}}:{{R}_{2}}:{{R}_{3}}=\frac{{{(3)}^{2}}}{1}:\frac{{{(2)}^{2}}}{2}:\frac{{{(1)}^{2}}}{3}\] \[=9:2:\frac{1}{3}=27:6:1\]
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