Mechanical Properties Of Solids Question 9
Question 9 - 2024 (31 Jan Shift 2)
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 $4.0 \times 10^{-5} \mathrm{~m}$ and Young’s modulus of the metal is $2.0 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$. The longitudinal strain developed in the wire is $\frac{1}{\alpha \pi}$. The value of $\alpha$ is [Use $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$ )
Show Answer
Answer: (12)
Solution:
$\mathrm{T}=\left(\frac{2 \mathrm{~m}{1} \mathrm{~m}{2}}{\mathrm{~m}{1}+\mathrm{m}{2}}\right) \mathrm{g}=\frac{80}{3} \mathrm{~N}$
$\mathrm{A}=\pi \mathrm{r}^{2}=16 \pi \times 10^{-10} \mathrm{~m}^{2}$
Strain $=\frac{\Delta \ell}{\ell}=\frac{F}{A Y}=\frac{T^{A Y}}{A Y}$
$=\frac{80 / 3}{16 \pi \times 10^{-10} \times 2 \times 10^{11}}=\frac{1}{12 \pi}$
$\alpha=12$
