A thick rope of density $\rho$ and length $L$ is hung from a rigid support. The Young's modulus of the material of rope is $Y$. The increase in length of the rope due to its own weight is
A thick rope of density $\rho$ and length $L$ is hung from a rigid support. The Young's modulus of the material of rope is $Y$. The increase in length of the rope due to its own weight is
- A
$(1 / 4) \rho gL ^2 / Y$
- B
$(1 / 2) \rho g L ^2 / Y$
- C
$\rho g L ^2 / Y$
- D
$\rho g L / Y$
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- [JEE MAIN 2022]