Question 22 of 118

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 $\frac{1}{3}^{\text {rd }}$ of the value on the surface of earth. The maximum length of the wire with breaking is _____ m (take, $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ ).

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Answer: 600

$\begin{aligned} & \mathrm{T}=\mathrm{mg} \\ & \sigma=\frac{\mathrm{T}}{\mathrm{A}}=\frac{\mathrm{mg}}{\mathrm{A}} \\ & \frac{(\sigma \mathrm{A} \ell) \mathrm{g}}{\mathrm{A}} \\ & \Rightarrow \ell=\frac{\sigma}{\rho \mathrm{g}}=\frac{1.2 \times 10^8 \times 3}{6 \times 10^4 \times 10}=600\end{aligned}$