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EEJ MAIN Physics QUESTION #7088
Question 1
A wire has length $l_1$ at tension $T_1$ and $l_2$ at tension $T_2$. Find its original length.
  • $\frac{T_1 l_1 - T_2 l_2}{T_2 - T_1}$
  • $\frac{l_1 + l_2}{2}$
  • $\frac{T_2 l_1 + T_1 l_2}{T_2 + T_1}$
  • $\frac{T_2 l_1 - T_1 l_2}{T_2 - T_1}$✔️
Correct Answer Explanation

Using Hooke's Law: $l = L + \frac{TL}{AY} \implies l = L + kT$ where $k = \frac{L}{AY}$.

  • $l_1 = L + kT_1$ and $l_2 = L + kT_2$
  • Subtracting: $l_2 - l_1 = k(T_2 - T_1) \implies k = \frac{l_2 - l_1}{T_2 - T_1}$
  • Substitute $k$ back: $L = l_1 - T_1(\frac{l_2 - l_1}{T_2 - T_1}) = \frac{T_2 l_1 - T_1 l_2}{T_2 - T_1}$.