A bar of mass m and length l is hanging from point A as shown in the figure. If the Young's modulus of elasticity of the bar is Y and area of cross-section of the wire is A , then the increase in its length due to its own weight will be

Question

A bar of mass m and length l is hanging from point A as shown in the figure. If the Young's modulus of elasticity of the bar is Y and area of cross-section of the wire is A , then the increase in its length due to its own weight will be, m g L 2 A Y, m g A 2 L Y, m g 2 L A Y, 2 L Y m g A

MARKS App · Accepted Answer

Consider a small section d x of the bar at a distance x from B. The weight of the bar for a length x is, W = m g L x . Elongation in x will be d e = W A Y d x = m g L A Y d x ⋅ x . Total elongation of the bar can be obtained by integrating this expression for x = 0 t o x = L . ∴ Δ l = ∫ x = 0 x = L d e = m g L A Y ∫ 0 L x ⋅ d x ⇒ Δ l = m g L 2 A Y

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