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8.Mechanical Properties of Solids
hard
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
$\frac{{2mg}}{{3A}}$
B
$\frac{{4mg}}{{3A}}$
C
$\frac{{mg}}{{A}}$
D
$\frac{{3mg}}{{4A}}$
(JEE MAIN-2013)
Solution
Tension in the wire, $T = \left( {\frac{{2mM}}{{m + M}}} \right)g.$
$Stress = \frac{{Force/Tension}}{{Area}} = \frac{{2mM}}{{A\left( {m + M} \right)}}g$
$ = \frac{{2\left( {m \times 2m} \right)g}}{{A\left( {m + 2m} \right)}}\left( {M = 2m\,given} \right)$
$ = \frac{{4{m^2}}}{{3mA}}g = \frac{{4mg}}{{3A}}$
Standard 11
Physics
