question_answer

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  \[\operatorname{M}=2\] m, then the stress produced in the wire is:                        [JEE ONLINE 25-04-2013]

A)        \[\frac{2\operatorname{mg}}{3A}\]       

B)       \[\frac{4\operatorname{mg}}{3A}\]

C)  \[\frac{\operatorname{mg}}{A}\]                        D)       \[\frac{3\operatorname{mg}}{4A}\] Correct Answer: B Solution : [b] Tension in the wire, \[T=\left( \frac{2mM}{m+M} \right)g\]

Stress\[=\frac{Force/Tension}{Area}=\frac{2mM}{A(m+M)}g\]

\[=\frac{2(m\times 2m)g}{A(m+2m)}=(M=2m\,\text{given})\]

\[=\frac{4{{m}^{2}}}{3mA}g=\frac{4mg}{3A}\]