Question

We have two wires $W_1 $ and $ W_2$. Both are made of same material and have the same length. The radius of cross-section $W_2$ is twice that of $W_1$. Same load is suspended from both of them. If the strain in $W_1$ be 4, then that in $W_2$ will be

• A. 1
• B. 2
• C. 4
• D. 8

Answer 1

Answer: (A)

using, $\frac{ F }{ A }= Y \frac{\Delta l _{1}}{ l _{1}}$
$\quad \frac{ F }{\pi r ^{2}}= Y (4) \longrightarrow $ for $W _{1}$
$\Rightarrow F =4 \pi r ^{2} Y$
for $W _{2} \longrightarrow $
$\frac{4 \pi r ^{2} Y }{4 \pi r ^{2}}= Y \frac{\Delta l _{2}}{ l _{2}}$
$\Rightarrow \frac{\Delta l _{2}}{ l _{2}}=1$