Question 237: Properties of Matter

Question

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

Accepted Answer

$$\begin{aligned}
& \mathrm{T}=\left(\frac{2 \mathrm{~m}_1 \mathrm{~m}_2}{\mathrm{~m}_1+\mathrm{m}_2}ight) \mathrm{g}=\frac{80}{3} \mathrm{~N} \
& \mathrm{~A}=\pi \mathrm{r}^2=16 \pi 	imes 10^{-10} \mathrm{~m}^2 \
& 	ext { Strain }=\frac{\Delta \ell}{\ell}=\frac{\mathrm{F}}{\mathrm{AY}}=\frac{\mathrm{T}}{\mathrm{AY}} \
& =\frac{80 / 3}{16 \pi 	imes 10^{-10} 	imes 2 	imes 10^{11}}=\frac{1}{12 \pi} \
& \alpha=12
\end{aligned}$$

Properties of Matter

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