Q 11-08-036JEE MainJEE Main 2024 (5 Apr, Shift 1)Easy
The density and breaking stress of a wire are $6\times10^4\ \text{kg/m}^3$ and $1.2\times10^8\ \text{N/m}^2$ respectively. The wire is suspended from a rigid support on a planet where the acceleration due to gravity is $\dfrac13$ of the value on the surface of the earth. The maximum length of the wire without breaking is ______ m (take $g = 10\ \text{m/s}^2$).
Numerical value type. Enter your answer.
Answer: 600
The stress at the top of a hanging wire of length $L$ is $\rho g' L$:
$$L = \frac{\text{breaking stress}}{\rho g'} = \frac{1.2\times10^8}{6\times10^4\times10/3} = \frac{1.2\times10^8}{2\times10^5} = 600\ \text{m}$$
Solution by Sreeraj P, M.Sc Physics