check the statment are True or False $:$
$(a)$ Young’s modulus of rigid body is .....
$(b)$ A wire increases by $10^{-6}$ times its original length when a stress of
$10^8\,Nm^{-2}$ is applied to it, calculate its Young’s modulus.
$(c)$ The value of Poisson’s ratio for steel is ......
check the statment are True or False $:$
$(a)$ Young’s modulus of rigid body is .....
$(b)$ A wire increases by $10^{-6}$ times its original length when a stress of
$10^8\,Nm^{-2}$ is applied to it, calculate its Young’s modulus.
$(c)$ The value of Poisson’s ratio for steel is ......
$(1)$ Infinite.
There is no strain in rigid body.
$\text { hence Young's modulus } =\frac{\text { stress }}{\text { strain }}=\frac{\text { stress }}{0}$
$=\text { infinite }$
$(2)$ $10^{14} \mathrm{Nm}^{2}$
$\mathrm{Y}=\frac{\text { Stress }}{\frac{\Delta l}{l}}=\frac{10^{8}}{10^{-6}}=10^{14} \mathrm{Nm}^{-2}$
$(3)$ $0.28$ to $0.30$
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- [JEE MAIN 2023]
$(a)$ A steel wire of mass $\mu $ per unit length with a circular cross section has a radius of $0.1\,cm$. The wire is of length $10\,m$ when measured lying horizontal and hangs from a hook on the wall. A mass of $25\, kg$ is hung from the free end of the wire. Assuming the wire to be uniform an lateral strains $< \,<$ longitudinal strains find the extension in the length of the wire. The density of steel is $7860\, kgm^{-3}$ and Young’s modulus $=2 \times 10^{11}\,Nm^{-2}$.
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