Question

All the edges of a block with parallel faces are unequal. Its longest edge is twice its shortest edge. The ratio of the maximum to minimum resistance between parallel faces is

• A. 2
• B. 4
• C. 8
• D. indeterminate unless the length of the third edge is specified

Answer 1

The correct option is B 4

Let the edges be $2l,a$ and $l$ in decreasing order.
We know that resistance, $R=\frac{\rho l}{A}$
Here, $l_{max}=2l,A_{max}=2la$ and $l_{min}=l,A_{min}=la$

Thus, $R_{max}=\frac{\rho l_{max}}{A_{min}}=\frac{\rho 2l}{la}=\frac{2\rho }{a}$ and $R_{min}=\frac{\rho l_{min}}{A_{max}}=\frac{\rho l}{2la}=\frac{\rho }{2a}$

$⟹\frac{R_{max}}{R_{min}}=4$