Q 11-08-035JEE MainJEE Main 2024 (4 Apr, Shift 1)Medium
An elastic spring under a tension of $3\ \text{N}$ has a length $a$. Its length is $b$ under a tension of $2\ \text{N}$. For its length $(3a - 2b)$, the value of the tension will be ______ N.
Numerical value type. Enter your answer.
Answer: 5
Let the natural length be $l_0$ and spring constant $k$: $3 = k(a - l_0)$ and $2 = k(b - l_0)$.
Subtracting: $k = \dfrac{1}{a - b}$, and $l_0 = a - 3(a - b) = 3b - 2a$.
$$T = k\big[(3a - 2b) - (3b - 2a)\big] = \frac{5(a - b)}{a - b} = 5\ \text{N}$$
Solution by Sreeraj P, M.Sc Physics