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 at a rigid support. The tensile stress a distance x from support is ( A- 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 $\frac{Mg+mg(l-x)}{A}$

The correct option is A.

We have,

Length$=L$

Mass$=m$

Distance$=x$m

So,

Tensile stress $=\frac{Tension}{Area}$

Tension at distance x from the 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$+mg$

Therefore,

Tensile stress$=\frac{mg(1-x)+mg}{A}$