Question

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

• A. The extension of $A$ will be twice that of $B$
• B. The extensions of $A$ and $B$ will be equal
• C. The strain in $A$ will be half that is $B$
• D. The strains in $A$ and $B$ will be equal

Answer 1

Answer: (A), (D)

The correct options are
A The extension of $A$ will be twice that of $B$
D The strains in $A$ and $B$ will be equal

$Y=\frac{F/A}{\Delta l/l}$
$Y=\frac{F/A}{\Delta l_A/l_A}$----(1)
$Y=\frac{F/A}{\Delta l_B/l_B}$-----(2)
dividing (1) by (2)
$1=\frac{l_A}{\Delta l_A}\times \frac{\Delta l_B}{l_B}$------(3)
$2=\frac{l_A}{l_B}=\frac{\Delta l_A}{\Delta l_B}$
$\therefore \Delta l_A=2\Delta l_B$
So, extension in A is twice and strain is same in A and B by (3) equation.