The density and breaking stress of a wire are 6 × 10⁴ kg/m³ and 1.2 × 10⁸ N/m² respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is 1/3 rd of the value on the surface of earth. The maximum length of the wire without breaking is _______ m (take, g = 10 m/s²). Numerical answer type. Work it out, then open the answer.

Answer: 600. Wire breaks at the top under its own weight: ρ L g' = S ⇒ L = (S)/(ρ g'). g' = 10/3 m/s² L = (1.2 × 10⁸)/(6 × 10⁴ × 10/3) = (1.2 × 10⁸)/(2 × 10⁵) = 600 m So the answer is 600 m.

The density and breaking stress of a wire are 6 × 10⁴ kg/m³ and 1.2 ×… | JEE Main 2024 (5 Apr, Shift 1)

Q5JEE Main 2024 · 5 APR · SHIFT 1Medium

Thermal Stress & Breaking Stress

The density and breaking stress of a wire are $6 \times 10^{4}\text{ kg/m}^3$ and $1.2 \times 10^{8}\text{ N/m}^2$ respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is $\frac{1}{3}$ rd of the value on the surface of earth. The maximum length of the wire without breaking is _______ $\text{m}$ (take, $\text{g} = 10\text{ m/s}^2$ ).

Numerical answer type. Work it out, then open the answer.

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Answer: 600

Wire breaks at the top under its own weight: $\rho L g' = S \Rightarrow L = \dfrac{S}{\rho g'}$ .
$g' = \dfrac{10}{3}\text{ m/s}^2$
$L = \dfrac{1.2 \times 10^8}{6 \times 10^4 \times 10/3} = \dfrac{1.2 \times 10^8}{2 \times 10^5} = 600\text{ m}$
So the answer is 600 m.

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