Question

Two wires $A$ and $B$ have equal lengths and are made of the same material, but the diameter of $A$ is twice that of wire $B$. Then, for a given load,

• A. the extension of $B$ will be four times that of $A$.
• B. the extension of $A$ and $B$ will be equal.
• C. the strain in $B$ is four times that in $A$.
• D. the strains in $A$ and $B$ will be equal.

Answer 1

Answer: (A), (C)

The correct options are
A the extension of $B$ will be four times that of $A$.
C the strain in $B$ is four times that in $A$.

As $r=\frac{d}{2}$
Therefore, $\Delta l=\frac{Fl}{AY}$ = $\frac{Fl}{\pi \frac{d^2}{4}Y}$..........(1)
$\frac{\Delta l}{l}=\frac{4F}{\pi d^{2}Y}$
Therefore, Strain $\propto \frac{1}{l^2}$.........(2)
Since diameter of $A$ is twice that of $B$, from (1) the extension of $B$ will be four times that of $A$
From (2), strain in $B$ is 4 times that of $B$