Question

A block of metal is made in the cuboid form with all edges of unequal lengths such that the shortest length is one third the longest one. if $R_{max}$ and $R_{min}$ are the maximum and minimum resistance between parallel faces then choose the correct relation.

• A. $\frac{R_{max}}{R_{min}}=\frac{3}{2}$
• B. $\frac{R_{max}}{R_{min}}=\frac{3}{1}$
• C. $\frac{R_{max}}{R_{min}}=\frac{9}{1}$
• D. $\frac{R_{max}}{R_{min}}=\frac{2}{1}$

Answer 1

The correct option is C $\frac{R_{max}}{R_{min}}=\frac{9}{1}$

$\begin{array}{c}Accordingtoquestion.\\ Resistanceisdirectlyproportionaltolength\left(L\right)butinverslhyproportionalto\\ normalarea.\left(A\right),\\ therefore,Resistance\left(R\right)=K\left(\frac{L}{A}\right)\left[whereKisconstantofproportional\right]\\ Now,considera,b,andcaresidesofgivencuboidwith:\\ \Rightarrow 3\times a=c|whereabeingshortest\&cbeinglongestside\\ let,littleconsiderationwillshowyouRminwillbealongaacrossb\times c.\\ similarly,Rmaxwillbealongcacrossa\times b.\\ sothat,Rmin=k\left(\frac{a}{b\times c}\right)=k\left(\frac{a}{b\times 3\times a}\right)=k\left(\frac{1}{3b}\right)\\ and,\\ Rmax=k\left(\frac{c}{a\times b}\right)=k\left(\frac{3a}{a\times b}\right)=k\left(\frac{3}{b}\right)\\ Now,\\ \Rightarrow \frac{Rman}{Rmix}=\frac{k\left(\frac{3}{b}\right)}{k\left(\frac{1}{3b}\right)}=\\ \therefore \frac{Rman}{Rmix}=\frac{9}{1}\\ sothatthecorrectoptionisC.\end{array}$