A thick rope of density ρ and length L is hung from a rigid support. The increase in length of the rope…

Q: A thick rope of density ρ and length L is hung from a rigid support. The increase in length of the rope due to its own weight is (Y is the Young’s modulus)

(a) \displaystyle \frac{1}{4Y}\rho L^2 g

(b) \displaystyle \frac{1}{2Y}\rho L^2 g

(c) \displaystyle \frac{\rho L^2 g}{Y}

(d) \displaystyle \frac{\rho L g}{Y}

Ans: (b)

Tension at mid is

T = Mg/2

Young’s modulus of Elasticity is

\displaystyle Y = \frac{T L}{A \Delta L}

\displaystyle \Delta L = \frac{T L}{A Y}

\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}

Author: Rajesh Jha

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