Question

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

• A. \( 3 : 1 \)
• B. \( 1 : 3 \)
• C. \( 9 : 1 \)
• D. \( 1 : 1 \)

Hint:

The resistance of a material is inversely proportional to its cross-sectional area.

Answer 1

The Correct Option is B

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: \[ R_1 : R_2 = \frac{1}{l^2} : \frac{1}{(3l)^2} \quad \Rightarrow \quad R_1 : R_2 = 9 : 1. \]