Question

A vertical hanging bar of length $l$ and mass $m$ 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 ( $A \rightarrow$ area of cross-section of bar)

• A. $\frac{M g+m g(l-x)}{A}$
• B. $\frac{M g}{A}$
• C. $\frac{M g+m g l}{A}$
• D. $\frac{(M+m) g x}{A l}$

Answer 1

Answer: (A)

Tensile stress $=\frac{\text { Tension at point }}{\text { Area }}$
Tension at distance $x$ from top would be the amount of force acting due to all the weight below it
$=$ Mass per unit length of rod $ \times$ length of rod $+M g$
$=m \times(l-x) g+M g$
So Tensile stress $=\frac{m(l-x) g+M g}{A}$