The density and breaking stress of a wire are and respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is of the value on the surface of Earth. The maximum length of the wire with breaking is _____ m (t

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Solution

Q.
The density and breaking stress of a wire are $6 \times 10^{4}$ $kg / m^{3}$ and $1.2 \times 10^{8}$ $N / m^{2}$ respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is $\frac{1}{3} r d$ of the value on the surface of Earth. The maximum length of the wire with breaking is _____ m (take, g = 10 $m / s^{2}$ ). [2024]

Ans.
(600)

$T = m g$

$σ = \frac{T}{A} = \frac{m g}{A} = \frac{(ρ A ℓ) g}{A}$

$\Rightarrow ℓ = \frac{σ}{ρ g} = \frac{1.2 \times 10^{8} \times 3}{6 \times 10^{4} \times 10} = 600$

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