Search any question & find its solution
Question:
Answered & Verified by Expert
A copper and a steel wire of the same diameter are connected end to end. A deforming force $F$ is applied to this composite wire which causes a total elongation of 1 $\mathrm{cm}$. The two wires will have
Options:
Solution:
1765 Upvotes
Verified Answer
The correct answers are:
the same stress
,
different strain
the same stress
,
different strain
Consider the given diagram where a deforming force $F$ is applied to the combination.
For steel Wire, $Y_{\text {steel }}=\frac{\text { Stress }}{\text { Strain }}=\frac{F / A}{\text { Strain }}$
where $F$ is force same in each wire and $A$ is crosssection area of each wires.
As $F$ and $A$ are same for both the wire, hence, their stress will be same for both the wire.
$$
\begin{aligned}
&(\text { Strain })_{\text {steel }}=\frac{\text { Stress }}{Y_{\text {steel }}},(\text { Strain })_{\text {copper }}=\frac{\text { Stress }}{Y_{\text {copper }}} \\
&\text { As, } \frac{(\text { Strain })_{\text {steel }}}{(\text { Strain })_{\text {copper }}}=\frac{Y_{\text {copper }}}{Y_{\text {steel }}}
\end{aligned}
$$
So, $Y_{\text {copper }} < Y_{\text {steel }}$
$(\text { Strain })_{\text {steel }} < (\text { Strain })_{\text {copper }}$
Hence, the two wires will have different strain.
For steel Wire, $Y_{\text {steel }}=\frac{\text { Stress }}{\text { Strain }}=\frac{F / A}{\text { Strain }}$
where $F$ is force same in each wire and $A$ is crosssection area of each wires.
As $F$ and $A$ are same for both the wire, hence, their stress will be same for both the wire.
$$
\begin{aligned}
&(\text { Strain })_{\text {steel }}=\frac{\text { Stress }}{Y_{\text {steel }}},(\text { Strain })_{\text {copper }}=\frac{\text { Stress }}{Y_{\text {copper }}} \\
&\text { As, } \frac{(\text { Strain })_{\text {steel }}}{(\text { Strain })_{\text {copper }}}=\frac{Y_{\text {copper }}}{Y_{\text {steel }}}
\end{aligned}
$$
So, $Y_{\text {copper }} < Y_{\text {steel }}$
$(\text { Strain })_{\text {steel }} < (\text { Strain })_{\text {copper }}$
Hence, the two wires will have different strain.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.