Question

One end of a uniform wire of length L and of weight W is attached rigidly to a point in the roof and a weight W1 is suspended from its lower end. of S is true area of cross section of the wire, the stress in the wire at a height (3L/4) from its lower end is:

• A. [W1 + (W/4)]/S
• B. W1/S
• C. [W1 + (3W/4)]/S
• D. (W1 + W)/S

Answer 1

The correct option is C [W1 + (3W/4)]/S

$\begin{array}{c}\text{Given, weight of wire}=W\\ \text{length of wire}=L\\ \text{Area of cross - section = Since, the wire has a}\\ \text{uniform mass density so weight of}\left(\frac{3L}{4}\right)\text{part of wire}\\ \text{is}\frac{3W}{4}.\end{array}$

$\begin{array}{c}\text{Total force at point}A:\frac{3W}{4}+W_1\\ \text{Stress in the wire at}\\ \text{point}A\text{is}:\frac{[W_1+\frac{3W}{4}]}{S}\end{array}$