Q 11-08-083JEE MainJEE Main 2021 (20 Jul, Shift 1)Medium
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:
Answer: (A) $\frac{T_1\ell_2 - T_2\ell_1}{T_1 - T_2}$
Extension is proportional to tension: $\ell = \ell_0 + cT$. So $\ell_1 = \ell_0 + cT_1$ and $\ell_2 = \ell_0 + cT_2$.
Eliminating $c$: $T_2(\ell_1 - \ell_0) = T_1(\ell_2 - \ell_0)$
$$\ell_0 = \frac{T_1\ell_2 - T_2\ell_1}{T_1 - T_2}$$
Solution by Sreeraj P, M.Sc Physics