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in Physics by (51.1k points)

A uniform rod of mass m, length L, area of cross-section A and Young’s modulus Y hangs from the ceiling. Its elongation under its own weight will be 

(a) zero

(b) mgL/2AY

(c) mgL/AY

(d) 2mgL/AY

1 Answer

+1 vote
by (50.3k points)
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Best answer

Correct Answer is: (b) mgL/2AY

Mass of section BC m/L (L - y).

∴ tension at B = T = m/L (L - y) g.

∴ elongation of element dy at B

= dx = (dy) T/AY = m/L (L - y)g dy/AY.

Total elongation =∫ dx = mg/LAY∫L0 (L- y) dy = mgL/2YA.

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