Question:

The sides of two solid cubes of the same material are \(l\) and \(3l\) respectively. The ratio of their resistances will be: 
 

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The resistance of a material is inversely proportional to its cross-sectional area.
Updated On: Mar 4, 2025
  • \( 3 : 1 \)
  • \( 1 : 3 \)
  • \( 9 : 1 \)
  • \( 1 : 1 \)
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The Correct Option is B

Solution and Explanation

The resistance \(R\) of a material is given by: \[ R \propto \frac{1}{\text{Cross-sectional area}}. \] For a cube, the cross-sectional area scales with \(l^2\), and resistance is inversely proportional to the square of the side length: \[ R_1 : R_2 = \frac{1}{l^2} : \frac{1}{(3l)^2} \quad \Rightarrow \quad R_1 : R_2 = 9 : 1. \]
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