Q 11-08-086JEE MainJEE Main 2021 (26 Feb, Shift 2)Medium
The length of metallic wire is $l_1$ when tension in it is $T_1$. It is $l_2$ when the tension is $T_2$. The original length of the wire will be:
Answer: (C) $\frac{T_2l_1-T_1l_2}{T_2-T_1}$
Let the original length be $L$. Extension is proportional to tension: $l_1 - L = kT_1$ and $l_2 - L = kT_2$.
Dividing: $\dfrac{l_1 - L}{l_2 - L} = \dfrac{T_1}{T_2} \Rightarrow T_2l_1 - T_2L = T_1l_2 - T_1L$
$$L = \frac{T_2l_1 - T_1l_2}{T_2 - T_1}$$
Solution by Sreeraj P, M.Sc Physics