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Physics Question on Applications of elastic behaviour of materials

A thick metal wire of density A thick metal wire of density ρ and length ‘L’ is hung from a rigid support. The increase in length of the wire due to its own weight is (Y=Young’s modulus of the material of the wire)and length ‘L’ is hung from a rigid support. The increase in length of the wire due to its own weight is (Y=Young’s modulus of the material of the wire)

A

ρgLY\frac{ρgL}{Y}

B

12ρgL2Y\frac{1}{2}\frac{ρgL^2}{Y}

C

ρgL2Y\frac{ρgL^2}{Y}

D

14ρgL2Y\frac{1}{4}\frac{ρgL^2}{Y}

Answer

12ρgL2Y\frac{1}{2}\frac{ρgL^2}{Y}

Explanation

Solution

The correct answer is Option (B) : 12ρgL2Y\frac{1}{2}\frac{ρgL^2}{Y}