Question

Two blocks of masses $m$ and $M$ are connected by means of a metal wire of cross-sectional area $A$ passing over a frictionless fixed pulley as shown in the figure. The system is then released. If $M \,= \,2 m$, then the stress produced in the wire is:

• A. $\frac{2 m g}{3 A}$
• B. $\frac{4 m g}{3 A}$
• C. $\frac{m g}{A}$
• D. $\frac{3 mg}{4 A}$

Answer 1

Answer: (B)

Tension in the wire, $T \approx \left(\frac{2 m M}{m+M}\right) g$
Stress =$\frac{Force/Tension }{Area}=\frac{2 m M}{A \left(m+M\right)} g$
$=\frac{2\left(m \times2m\right)}{A \left(m+2 m\right)} $ (M = 2mgiven)
$=\frac{4 m^{2}}{3 m A} g =\frac{4 m g}{3 A}$