Elongation Due to Self-Weight MCQ with answer and solution

Concept

A bar under its own weight stretches half as much as when its full weight hangs at the free end.

Formula

δ_self = WL/(2AE), δ_end = WL/(AE)

Step-by-step solution

1. Let total weight of bar = W, length = L, area = A, modulus = E. 2. Elongation due to self-weight: δ₁ = WL/(2AE). 3. Elongation when W acts at the end: δ₂ = WL/(AE). 4. Ratio δ₁/δ₂ = (WL/2AE)/(WL/AE) = 1/2.

Explanation

Under self-weight, the force in the bar grows from zero at the free end to W at the support, so the average force is W/2. With W at the end, the full force W acts over the whole length. So self-weight elongation is half.

Why the other options are wrong

B (2) is the inverse ratio. C (1/3) and D (3) have no basis for a prismatic bar; the factor 1/3 relates to the volume of a cone, not to this case.

Shortcut

Self-weight acts like W/2 at the end, so the ratio is 1/2.

Common mistake

Writing the ratio upside down (2 instead of 1/2).