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  • A thick rope of rubber of density <img alt="1.5 \times 10^3 \mathrm{~kg} / \mathrm{m}^3" src="https://entrancecorner.oncodecogs.com/gif.latex?1.5%20%5Ctimes%2010%5E3%20%5Cmathrm%7B%7Ekg%7D%20/

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

Option: 1

96 \times 10^{-3} \mathrm{~m}


Option: 2

19.2 \times 1 \mathrm{0}^{-5} \mathrm{~m}


Option: 3

9.4cm


Option: 4

9.6mm


Answers (1)

best_answer

Due to own weight, \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}{2Y}

\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}

\Delta l=9.4 \mathrm{~cm}

Posted by

vishal kumar

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