The length of a metal is \[{{\ell }_{1}}\] when the tension in it is\[{{T}_{1}}\]and is\[{{\ell }_{2}}\]when the tension is\[{{T}_{2}}\]. The original length of the wire is

\[\sqrt{{{T}_{1}}{{T}_{2}}{{\ell }_{1}}{{\ell }_{2}}}\]

\[\frac{{{\ell }_{1}}+{{\ell }_{2}}}{2}\]

\[\frac{{{\ell }_{1}}{{T}_{2}}+{{\ell }_{2}}{{T}_{1}}}{{{T}_{1}}+{{T}_{2}}}\]

(c)\[\frac{{{\ell }_{1}}{{T}_{2}}-{{\ell }_{2}}{{T}_{1}}}{{{T}_{2}}-{{T}_{1}}}\]

The length of a metal is \[{{\ell }_{1}}\] when the tension in it is\[

1.	The length of a metal is \[{{\ell }_{1}}\] when the tension in it is\[{{T}_{1}}\]and is\[{{\ell }_{2}}\]when the tension is\[{{T}_{2}}\]. The original length of the wire is
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.	\[\sqrt{{{T}_{1}}{{T}_{2}}{{\ell }_{1}}{{\ell }_{2}}}\]
Answer» D. \[\sqrt{{{T}_{1}}{{T}_{2}}{{\ell }_{1}}{{\ell }_{2}}}\]