Question

Length,width and height of a rectangular cuboid block are unequal. Its longest edge is twice its shortest edge. The ratio of the maximum to minimum resistance between parallel faces is

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

Answer 1

The correct option is A $4$

Let the edges be $2a,b$ and $a$ in decreasing order.

By formula of resistance

$R=\frac{\rho l}{A}$

For maximum resistance,

$A=ab;l=2a$

$R_{max}=\rho \frac{2a}{ab}=\frac{2\rho }{b}$

For minimum resistance,

$A=2ab;l=a$

$R_{min}=\frac{\rho a}{2ab}=\frac{\rho }{2b}$

$\therefore \frac{R_{max}}{R_{min}}=4$

Hence, option $\left(b\right)$ is correct.