Question

A vertical hanging bar of length $l$ and mass density $m$ per unit length carries a load of mass $M$ at lower end, its upper end is clamped to a rigid support. The tensile stress a distance $x$ from support is ($A\to$ area of cross-section of bar).

• A. $\frac{Mg+mg(l-x)}{A}$
• B. $\frac{Mg}{A}$
• C. $\frac{Mg+mgl}{A}$
• D. $\frac{(M+m)gx}{Al}$

Answer 1

The correct option is A $\frac{Mg+mg(l-x)}{A}$

Mass of (l - x) part = m(l - x)

$\therefore$ Total force = force due to (l - x) part + force due to M = m(l - x)g + mg

$\therefore$ F = Mg + m(l - x)g

$\therefore$ Tensile stress = $\frac{Force}{Area}=\frac{Mg+mg(l-x)}{A}$