JEE Mains · Physics · STD 11- Mechanical properties of solids
- JEE Mains 2021
- Medium
- MCQ
Two wires of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are \(Y_{1}\) and \(Y_{2}\). The combination behaves as a single wire then its Young's modulus is:
Pick an option to check your answer.
Answer & Solution
Correct Answer
(C) \(Y=\frac{2 Y_{1} Y_{2}}{Y_{1}+Y_{2}}\)
Step-by-step Solution
Detailed explanation
In series combination \(\Delta l =l_{1}+l_{2}\)
\(Y =\frac{ F / A }{\Delta l / l} \Rightarrow \Delta l=\frac{ F l}{ AY }\)
\(\Rightarrow \Delta l \propto \frac{l}{ Y }\)
Equivalent length of rod after joining is \(=2 l\)
As, lengths are same and force is also same in series
\(\Delta l=\Delta l_{1}+\Delta l_{2}\)
\(\frac{l \text { eq }}{ Y _{\text {eq }}}=\frac{l}{ Y _{1}}+\frac{l}{ Y _{2}}\) \(\Rightarrow \frac{2 l}{ Y }=\frac{l}{ Y _{1}}+\frac{l}{ Y _{2}}\)
\(\therefore Y=\frac{2 Y_{1} Y_{2}}{Y_{1}+Y_{2}}\)
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