The value of tension in a long thin metal wire has been changed from $$T_1$$ to $$T_2$$. The lengths of the metal wire at two different values of tension $$T_1$$ and $$T_2$$ are $$\ell_1$$ and $$\ell_2$$, respectively. The actual length of the metal wire is:

A

$$\frac{T_1\ell_2 - T_2\ell_1}{T_1 - T_2}$$

B

$$\frac{T_1\ell_1 - T_2\ell_2}{T_1 - T_2}$$

C

$$\frac{\ell_1 + \ell_2}{2}$$

D

$$\sqrt{T_1 T_2 \ell_1 \ell_2}$$