Question

Two wires $A$ and $B$ have the same cross section and are made of the same material, but the length of wire $A$ is twice that of $B$. 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 in $B$
• 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

We know that $Y=\frac{FL}{Al}$
$\therefore l=\frac{FL}{AY}$
Since, the two wires are made of the same material, Young's modulus $Y$ is same for both. Since, load $F$ and the cross-sectional area $A$ are the same,
$\therefore l\propto L$
i.e., extension is proportional to the length of the wire.
Hence, option (a) is correct. The strain in a wire is given by
$\frac{l}{L}=\frac{4F}{AY}$
Since $F,A$ and $Y$ are the same, the strains in wires $A$ and $B$ will be equal. Thus, the correct options are (a) and (d).