Q76 / 90 · JEE Main 2021 (20 Jul Shift 1) · Physics

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 $ℓ_{1}$ and $ℓ_{2}$ , respectively. The actual length of the metal wire is:

Solution

Y = \frac{F L}{A Δ L}

\Rightarrow Y = \frac{T_{1} ℓ_{0}}{A (ℓ_{1} - ℓ_{0})} = \frac{T_{2} ℓ_{0}}{A (ℓ_{2} - ℓ_{0})}

1 = \frac{T_{1} (ℓ_{2} - ℓ_{0})}{T_{2} (ℓ_{1} - ℓ_{0})}

T_{2} ℓ_{1} - T_{2} ℓ_{0} = T_{1} ℓ_{2} - T_{1} ℓ_{0}

(T_{1} - T_{2}) ℓ_{0} = T_{1} ℓ_{2} - T_{2} ℓ_{1}

ℓ_{0} = (\frac{T_{1} ℓ_{2} - T_{2} ℓ_{1}}{T_{1} - T_{2}})

Hence, the correct answer is option: 'A'.