Question

One end of uniform wire of length L and of weight W is attached rigidly to a point in the roof and a weight $W_1$ is suspended from its lower end. If s is the area of cross section of the wire, the stress in the wire at a height $\frac{L}{4}$ from its lower end is -

• A. $\frac{W_1}{s}$
• B. $\frac{[W_1+\frac{W}{4}]}{s}$
• C. $\frac{[W_1+\frac{3W}{4}]}{s}$
• D. $\frac{W_1+W}{4}$

Answer 1

The correct option is B $\frac{[W_1+\frac{W}{4}]}{s}$

Consider the FBD as:

Let x be the weight of wire part of $l=l/4$

As wire is uniform,

$\frac{x}{\frac{l}{4}}=\frac{w}{l}$

$\Rightarrow x=w/4$

For equilibrium,

$F=w_1+x=w_1+w/4$

So stress at point P$=\frac{F}{s}=\frac{(w_1+w/4)}{s}$

option B is correct.