A thick uniform rubber of density 1.5 g cm^-3 and Young’s modulus 5 × 10^6 Nm-2 has a length of 8 m. When hung from the ceiling of a room. The increase in length of the rope due to its own weight will be

Q: A thick uniform rubber of density 1.5 g cm-3 and Young’s modulus 5 × 106 Nm-2 has a length of 8 m. When hung from the ceiling of a room. The increase in length of the rope due to its own weight will be (Given, g = 10 ms-2)

(a) 9.6 × 10-8 m

(b) 19.2 × 10-3 m

(c) 9.6 × 10-3 m

(d) 9.6 m

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Ans: (a)

$ \displaystyle \Delta L = \frac{M g L}{2A Y} $

$ \displaystyle \Delta L = \frac{(A L \rho ) g L}{2 A Y} $

$ \displaystyle \Delta L = \frac{\rho g L^2}{2 Y} $