Mechanical Properties Of Solids Question 9
Question 9 - 2024 (31 Jan Shift 2)
Two blocks of mass $2 kg$ and $4 kg$ are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is $4.0 \times 10^{-5} m$ and Young’s modulus of the metal is $2.0 \times 10^{11} N / m^{2}$. The longitudinal strain developed in the wire is $\frac{1}{\alpha \pi}$. The value of $\alpha$ is [Use $g=10 m / s^{2}$ )
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Answer: (12)
Solution:
$T=\left(\frac{2 m _1 m _2}{m _1+m _2}\right) g=\frac{80}{3} N$
$A=\pi r^{2}=16 \pi \times 10^{-10} m^{2}$
Strain $=\frac{\Delta \ell}{\ell}=\frac{F}{A Y}=\frac{T^{A Y}}{A Y}$
$=\frac{80 / 3}{16 \pi \times 10^{-10} \times 2 \times 10^{11}}=\frac{1}{12 \pi}$
$\alpha=12$
