A) \[\frac{({{Y}_{1}}{{Y}_{2}})A}{2({{Y}_{1}}{{L}_{2}}+{{Y}_{2}}{{L}_{1}})}\]
B) \[\frac{({{Y}_{1}}{{Y}_{2}})A}{{{({{L}_{1}}{{L}_{2}})}^{1/2}}}\]
C) \[\frac{({{Y}_{1}}{{Y}_{2}})A}{{{Y}_{1}}{{L}_{2}}+{{Y}_{2}}{{L}_{1}}}\]
D) \[\frac{{{({{Y}_{1}}{{Y}_{2}})}^{1/2}}A}{{{({{L}_{2}}{{L}_{1}})}^{1/2}}}\]
Correct Answer: C
Solution :
[c] Using the usual expression for the Young's modulus, the force constant for the wire can be written as \[k=\frac{F}{\Delta l}=\frac{YA}{L}\]where the symbols have their usual meanings. Now the two wires together will have an effective force constant \[\left[ \frac{{{k}_{1}}{{k}_{2}}}{{{k}_{1}}+{{k}_{2}}} \right]\] Substituting the corresponding lengths and the Young's moduli we get the answer.You need to login to perform this action.
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