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A thick rope of rubber of density 1.5\times 10^{3}\, kg/m^{3} and Young's modulus 5\times 10^{6}\, N/m^{2},  8 m in length, when hung from ceiling of a room, the increase in length due to its own weight is:

Option: 1

96\times 10^{-3}\, m


Option: 2

19.2\times 10^{-5}\, m


Option: 3

9.4 \, cm


Option: 4

9.6\, mm


Answers (1)

best_answer

\text { Due to own weight, } \begin{aligned} \Delta l & =\frac{m g l}{2 A Y} \\ \Delta l & =\frac{(l A \rho) g l}{2 A Y}=\frac{l^2 \rho g}{24} \\ \Delta l & =\frac{(8)^2\left(1.5 \times 10^3\right)(9.8)}{2 \times 5 \times 10^6} \\ \Delta l & =9.4 \times 10^{-2} \mathrm{~m} \\ \Rightarrow \Delta l & =9.4 \mathrm{~cm} \end{aligned}

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Ritika Kankaria

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