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in Physics by (69.2k points)

A bar of mass m and length l is hanging from point A as shown in figure. Find the increase in its length due to its own weight. The Young’s modulus of elasticity of the wire is Y and area of cross-section of the wire is A.

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Consider a small section dx of the bar at a distance x from B. The weight of the bar for a length xis,

Elongation in section dx will be

Total elongation in the bar can be obtained by integrating this expression for x = 0 to x = l .

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