A) \[{{T}_{1}}{{l}_{1}}+{{T}_{2}}{{l}_{2}}\]
B) \[\frac{{{l}_{1}}{{T}_{2}}-{{l}_{2}}{{T}_{1}}}{{{T}_{2}}-{{T}_{1}}}\]
C) \[\frac{{{l}_{1}}{{T}_{2}}+{{l}_{2}}{{T}_{1}}}{{{T}_{2}}+{{T}_{1}}}\]
D) \[\frac{{{T}_{2}}}{{{T}_{1}}}({{l}_{1}}+{{l}_{2}})\]
Correct Answer: B
Solution :
\[y=\frac{Fl}{A\Delta l}\] Y is constant. \[\therefore \] \[\Delta l\propto F\] \[{{l}_{1}}-l\propto {{T}_{1}}\] and \[{{l}_{2}}-l\propto {{T}_{2}}\] \[\therefore \] \[\frac{{{l}_{1}}-l}{{{l}_{2}}-l}=\frac{{{T}_{1}}}{{{T}_{2}}}\] \[{{l}_{1}}{{T}_{2}}-l{{T}_{2}}={{l}_{2}}{{T}_{1}}-l{{T}_{1}}\] \[l({{T}_{1}}-{{T}_{2}})={{l}_{2}}{{T}_{1}}-{{l}_{1}}{{T}_{2}}\] \[l=\frac{{{l}_{1}}{{T}_{1}}-{{l}_{1}}{{T}_{2}}}{{{T}_{1}}-{{T}_{2}}}\Rightarrow l=\frac{{{l}_{1}}{{T}_{2}}-{{l}_{2}}{{T}_{1}}}{{{T}_{2}}-{{T}_{1}}}\]
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