Question

The sides of a rectangular block are 2 cm, 3 cm and 4 cm. The ratio of the maximum to minimum resistance between its parallel faces is:

• A. 4
• B. 3
• C. 2
• D. 1

Answer 1

The correct option is A 4

We know, $R\propto \frac{l}{A}$
or, $R=\rho \frac{l}{A}$
So,
resistance between parallel sides of length 3 cm and 2 cm:
$R_1=\frac{\rho \times 4}{6}=\frac{2\rho }{3}$
of length 4 cm and 3 cm:
$R_2=\frac{\rho \times 2}{12}=\frac{\rho }{6}$
of length 4 cm and 2 cm:
$R_3=\frac{\rho \times 3}{8}=\frac{3\rho }{8}$
Therefore, required ratio:
$\frac{R_1}{R_2}=\frac{\frac{2\rho }{3}}{\frac{\rho }{6}}=\frac{4}{1}$