Question 27 of 118

Each of three blocks $P,Q$ and $R$ shown in figure has a mass of $3kg$. Each of the wire $A$ and $B$ has cross-sectional area $0.005{cm}^{2}$ and Young's modulus $2\times {10}^{11}N{m}^{-2}$. Neglecting friction, the longitudinal strain on wire $B$ is _____ $\times {10}^{-4}$. (Take $g=10m{s}^{-2}$)

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Answer: 2

Acceleration of the system, $a=\dfrac{3g}{9}=\dfrac{10}{3}m{s}^{-2}$
Now, for $R$ we can write
$30-{T}_{1}=3\times a$
$\Rightarrow {T}_{1}=20N$
Therefore, strain developed in wire $B$,
$\text{strain}=\dfrac{\text{stress}}{Y} =\dfrac{\dfrac{{T}_{1}}{A}}{Y}=\dfrac{\dfrac{20}{0.005\times {10}^{-4}}}{2\times {10}^{11}}$
$=2\times {10}^{-4}$