Question

One end of a uniform rod of mass $m_{1}$, uniform area of cross-section $A$ is suspended from the roof and mass $m$ is suspended from the other end. What is the stress at the mid point of the rod?

• A. $\left(m_{1}+m_{2}\right) g / A$
• B. $\left(m_{1}-m_{2}\right) g / A$
• C. $\left[\frac{\left(m_{1} / 2\right)+m_{2}}{A}\right] g$
• D. $\left[\frac{m_{1}+\left(m_{2} / 2\right)}{A}\right] g$

Answer 1

Answer: (C)

As, stress $=\left(\right.$ weight due to mass $m_{2}+$ half of the weight of rod)/area
$=\left(m_{2} g+m_{1} g / 2\right) / A=\left[\left(m_{1} / 2\right)+m_{2}\right] g / A$