A block has dimensions $1 \mathrm{~cm}, 2 \mathrm{~cm}$ and 3 cm . Ratio of the maximum resistance to…

A block has dimensions $1 \mathrm{~cm}, 2 \mathrm{~cm}$ and 3 cm . Ratio of the maximum resistance to minimum resistance between any pair of opposite faces of the block is
  1. $9: 1$
  2. $1: 9$
  3. $18: 1$
  4. $6: 1$

Solution

Resistance, $\mathrm{R}=\rho \frac{l}{\mathrm{~A}} \Rightarrow \mathrm{R} \propto \frac{l}{\mathrm{~A}}$ $\therefore \mathrm{R}_{\max }=\rho \cdot \frac{l_{\max }}{\mathrm{A}_{\min }}=\rho \cdot \frac{3}{1 \times 2}=\frac{3 \delta}{2}$ $\mathrm{R}_{\min }=\rho \cdot \frac{l_{\min }}{\mathrm{A}_{\max }}=\rho \cdot \frac{1}{2 \times 3}=\frac{\rho}{6} \quad \therefore \frac{\mathrm{R}_{\max }}{\mathrm{R}_{\min }}=\frac{3 \rho}{2} \times \frac{6}{\rho}=9: 1$

Asked in: AP EAMCET 2024 (20 May Shift 1)

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