A) \[\frac{{{\ell }_{1}}+{{\ell }_{2}}}{2}\]
B) \[\frac{{{\ell }_{1}}{{\operatorname{T}}_{2}}+{{\operatorname{T}}_{1}}{{\ell }_{2}}}{2}\]
C) \[\frac{{{\ell }_{1}}{{\operatorname{T}}_{2}}-{{\operatorname{T}}_{1}}{{\ell }_{2}}}{{{\operatorname{T}}_{1}}+{{\operatorname{T}}_{2}}}\]
D) \[\sqrt{{{\ell }_{1}}{{\ell }_{2}}}\]
Correct Answer: B
Solution :
\[\operatorname{For}{{1}^{st}}\,case{{T}_{1}}=k({{\ell }_{1}}-L)\] .....(1) \[\operatorname{For}{{2}^{\operatorname{nd}}}\,case{{T}_{2}}=k({{\ell }_{2}}-L)\] .....(2) \[\left( 1 \right)\div \left( 2 \right)\] \[{{\operatorname{T}}_{1}}\left( {{\ell }_{2}}-L \right)={{T}_{2}}{{\ell }_{1}}-{{T}_{2}}L\] \[{{\operatorname{T}}_{1}}{{\ell }_{2}}-{{\operatorname{T}}_{1}}L={{T}_{2}}{{\ell }_{1}}-{{T}_{2}}L\] \[\operatorname{L}=\frac{{{T}_{2}}{{\ell }_{1}}-{{\operatorname{T}}_{1}}{{\ell }_{2}}}{{{\operatorname{T}}_{2}}-{{\operatorname{T}}_{1}}}\]You need to login to perform this action.
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