A) \[\frac{{{\ell }_{1}}+{{\ell }_{2}}}{2}\]
B) \[\frac{{{\ell }_{1}}{{T}_{2}}+{{\ell }_{2}}{{T}_{1}}}{{{T}_{1}}+{{T}_{2}}}\]
C) (c)\[\frac{{{\ell }_{1}}{{T}_{2}}-{{\ell }_{2}}{{T}_{1}}}{{{T}_{2}}-{{T}_{1}}}\]
D) \[\sqrt{{{T}_{1}}{{T}_{2}}{{\ell }_{1}}{{\ell }_{2}}}\]
Correct Answer: C
Solution :
[c] If \[\ell \] is the original length of wire, then change in length of first wire, \[\Delta {{\ell }_{1}}=({{\ell }_{1}}-\ell )\] Change in length of second wire, \[\Delta {{\ell }_{2}}=({{\ell }_{2}}-\ell )\] Now, \[Y=\frac{{{T}_{1}}}{A}\times \frac{\ell }{\Delta {{\ell }_{1}}}=\frac{{{T}_{2}}}{A}\times \frac{\ell }{\Delta {{\ell }_{2}}}\] or\[\frac{{{T}_{1}}}{\Delta {{\ell }_{1}}}=\frac{{{T}_{2}}}{\Delta {{\ell }_{2}}}\,or\,\frac{{{T}_{1}}}{{{\ell }_{1}}-\ell }=\frac{{{T}_{2}}}{{{\ell }_{2}}-\ell }\] or \[{{T}_{1}}{{\ell }_{2}}-{{T}_{1}}\ell ={{T}_{2}}{{\ell }_{1}}-\ell {{T}_{2}}\] or \[\ell =\frac{{{T}_{2}}{{\ell }_{1}}-{{T}_{1}}{{\ell }_{2}}}{{{T}_{2}}-{{T}_{1}}}\]You need to login to perform this action.
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