Q 11-08-108JEE MainJEE Main 2025 (2 Apr, Shift 2)Easy
The length of a light string is $1.4\ \text{m}$ when the tension on it is $5\ \text{N}$. If the tension increases to $7\ \text{N}$, the length of the string is $1.56\ \text{m}$. The original length of the string is ______ m.
Numerical value type. Enter your answer.
Answer: 1
Within the elastic limit the extension is proportional to the tension: $T = k(l - l_0)$.
$$5 = k(1.4 - l_0),\qquad 7 = k(1.56 - l_0)$$
Dividing: $5(1.56 - l_0) = 7(1.4 - l_0) \Rightarrow 7.8 - 5l_0 = 9.8 - 7l_0 \Rightarrow 2l_0 = 2 \Rightarrow l_0 = 1\ \text{m}$
Solution by Sreeraj P, M.Sc Physics