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JEE Main 20245 AprilMorning Shift
Exam
JEE Main
Year
2024
Date
5 April
Shift
Morning Shift
Subject
Physics
Chapter
Mechanical Properties of Solids

JEE Main 2024 · 5 April · Morning Shift · Physics · Mechanical Properties of Solids

The density and breaking stress of a wire are 6 × 10^4 ~kg / m^3...

The density and breaking stress of a wire are 6×104 kg/6 \times 10^4 \mathrm{~kg} /m3\mathrm{m}^3andand1.2 \times 10^8  N\mathrm{~N} / m2\mathrm{m}^2 respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is 13rd \frac{1}{3}^{\text{rd }} of the value on the surface of earth. The maximum length of the wire with breaking is _____ m (take, g=10 m/\mathrm{g}=10 \mathrm{~m} /s2\mathrm{s}^2).).The density and breaking stress of a wire are 6 × 10^4 ~kg / m^3 and 1.2 × 10^8 ~N / m^2 respectively. The wire is

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Step-by-step solution

The density and breaking stress of a wire are 6 × 10^4 ~kg / m^3 and 1.2 × 10^8 ~N / m^2 respectively. The wire is
T=mgσ=TA=mgA(σAℓ)gA⇒ℓ=σρg=1.2×108×36×104×10=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}
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