Question 26 of 118

Two blocks of mass $2kg$ and $4kg$ are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is $4.0\times {10}^{-5}m$ and Young's modulus of the metal is $2.0\times {10}^{11}N{m}^{-2}$. The longitudinal strain developed in the wire is $\dfrac{1}{\alpha \pi }$. The value of $\alpha$ is _____. [Use $g=10m{s}^{-2}$)

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Answer: 12

For the given system, $T=\left(\dfrac{2{m}_{1}{m}_{2}}{{m}_{1}+{m}_{2}}\right)g=\dfrac{80}{3}N$
Area of the wire, $A=\pi {r}^{2}=16\pi \times {10}^{-10}{m}^{2}$
Strain $=\dfrac{\Delta l}{l}=\dfrac{F}{AY}=\dfrac{T}{AY}$
$=\dfrac{\dfrac{80}{3}}{16\pi \times {10}^{-10}\times 2\times {10}^{11}}=\dfrac{1}{12\pi }$
$\Rightarrow \alpha =12$