Evaluate the following statements:
$(a)$ Young's modulus of a rigid body is .....
$(b)$ $A$ wire increases by $10^{-6}$ times its original length when a stress of $10^8 \ N/m^2$ is applied to it. Calculate its Young's modulus.
$(c)$ The value of Poisson's ratio for steel is ......
$(a)$ Young's modulus of a rigid body is .....
$(b)$ $A$ wire increases by $10^{-6}$ times its original length when a stress of $10^8 \ N/m^2$ is applied to it. Calculate its Young's modulus.
$(c)$ The value of Poisson's ratio for steel is ......
(N/A) The Young's modulus of a rigid body is infinite. Since there is no strain in a rigid body,$Y = \frac{\text{stress}}{\text{strain}} = \frac{\text{stress}}{0} = \infty$.
$(b)$ Given: $\frac{\Delta l}{l} = 10^{-6}$ and $\text{stress} = 10^8 \ N/m^2$.
Using the formula $Y = \frac{\text{stress}}{\text{strain}} = \frac{10^8}{10^{-6}} = 10^{14} \ N/m^2$.
$(c)$ The value of Poisson's ratio for steel typically ranges from $0.28$ to $0.30$.
$(b)$ Given: $\frac{\Delta l}{l} = 10^{-6}$ and $\text{stress} = 10^8 \ N/m^2$.
Using the formula $Y = \frac{\text{stress}}{\text{strain}} = \frac{10^8}{10^{-6}} = 10^{14} \ N/m^2$.
$(c)$ The value of Poisson's ratio for steel typically ranges from $0.28$ to $0.30$.
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