Q. One end of a uniform rod of mass $m_{1},$ uniform area of cross section A is suspended from the roof and mass $m_{2}$ 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) $\left\lbrack \frac{\left( m_{1}/2 \right) + m_{2}}{A} \right\rbrack$ g
D) $\left\lbrack \frac{m_{1} + \left( m_{2}/2 \right)}{A} \right\rbrack$ g
Explanation
(c) Stress = (weight due to mass $m_{2} + \ $half of the weight of rod)/area
= $\left( m_{2}g + m_{1}g/2 \right)/A$ =$\left\lbrack \left( m_{1}/2 \right) + \ m_{2} \right\rbrack g/A$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.