The density and breaking stress of a wire are $6 \times$ $10^4 \mathrm{~kg} / \mathrm{m}^3$ and $1.2 \times 10^8 \mathrm{~N} / \mathrm{m}^2$ respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is $\frac{1^{\text {rd }}}{3}$ of the value on the surface of earth. The maximum length of the wire with breaking is ............ $\mathrm{m}$ (take, $\mathrm{g}=$ $\left.10 \mathrm{~m} / \mathrm{s}^2\right)$
JEE MAIN 2024, Diffcult
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$\mathrm{T}=\mathrm{mg}$
$\sigma=\frac{\mathrm{T}}{\mathrm{A}}=\frac{\mathrm{mg}}{\mathrm{A}}$
$\frac{(\sigma \mathrm{A} \ell) \mathrm{g}}{\mathrm{A}}$
$\Rightarrow \ell=\frac{\sigma}{\rho \mathrm{g}}=\frac{1.2 \times 10^8 \times 3}{6 \times 10^4 \times 10}=600$
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