Question

When a load is attached at the midpoint of a steel bar A of length \(80\,\text{cm}\), breadth \(2.5\,\text{cm}\) and thickness \(2\,\text{mm}\), it sags by \(1.2\,\text{mm}\). If the same load is attached at the midpoint of another steel bar B of length \(120\,\text{cm}\), breadth \(3\,\text{cm}\) and thickness \(3\,\text{mm}\), then the bar B sags by \[ (\text{In both the cases, the bars are supported at the two ends}) \]

• A. \(0.18\,\text{cm}\)
• B. \(0.10\,\text{cm}\)
• C. \(0.12\,\text{cm}\)
• D. \(0.15\,\text{cm}\)

Hint:

For a simply supported rectangular beam carrying a central load, \[ \boxed{ y\propto\frac{L^3}{bd^3}. } \] The sag increases rapidly with the length of the beam and decreases with the cube of its thickness.

Answer 1

The Correct Option is B