Question

When a uniform bar of length \(l\), breadth \(b\) and thickness \(d\) is supported by rigid supports near the ends and loaded at the centre by a vehicle of mass \(M\), the bar sags by an amount \(\delta\). If \(Y\) is the Young's modulus of the material, then \(\delta\) is

• A. \[ \frac{Ml^3}{4bd^3Y} \]
• B. \[ \frac{Yl^3}{4Mgbd^3} \]
• C. \[ \frac{Yd^3}{4Mgl^3b} \]
• D. \[ \frac{Mgl^3}{4bd^3Y} \]

Hint:

For a rectangular beam supported at both ends and loaded at the centre, \[ \delta=\frac{Wl^3}{4Ybd^3}. \] Remember that the depression is directly proportional to the load and cube of the length, and inversely proportional to \(Y\) and \(d^3\).

Answer 1

The Correct Option is D