The relation between Young's modulus (Y),modu | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The relations between elastic constants are given by:$Y = 3K(1 - 2\sigma)$  --- $(1)$$Y = 2\eta(1 + \sigma)$  --- $(2)$From $(1)$,we have: $\frac{

Vedclass · Accepted Answer

$\frac{1}{Y} = \frac{1}{3\eta} + \frac{1}{9K}$

Vedclass · Answer

(D) The relations between elastic constants are given by:$Y = 3K(1 - 2\sigma)$  --- $(1)$$Y = 2\eta(1 + \sigma)$  --- $(2)$From $(1)$,we have: $\frac{Y}{3K} = 1 - 2\sigma$  --- $(3)$From $(2)$,we have: $\frac{Y}{2\eta} = 1 + \sigma$  --- $(4)$To eliminate $\sigma$,multiply equation $(4)$ by $2$:$\frac{Y}{\eta} = 2 + 2\sigma$  --- $(5)$Adding equations $(3)$ and $(5)$:$\frac{Y}{3K} + \frac{Y}{\eta} = (1 - 2\sigma) + (2 + 2\sigma)$$\frac{Y}{3K} + \frac{Y}{\eta} = 3$Dividing both sides by $3Y$:$\frac{1}{9K} + \frac{1}{3\eta} = \frac{1}{Y}$Thus,the correct relation is $\frac{1}{Y} = \frac{1}{3\eta} + \frac{1}{9K}$.

The relation between Young's modulus $(Y)$,modulus of rigidity $(\eta)$,and bulk modulus $(K)$ for an elastic material is:

Similar Questions

If the Young's modulus of a material is $2.4$ times its modulus of rigidity,what is the Poisson's ratio of the material?

$A$ cylindrical wire of radius $1\, mm$,length $1\, m$,Young's modulus $Y = 2 \times 10^{11}\, N/m^2$,and Poisson's ratio $\mu = \pi / 10$ is stretched by a force of $100\, N$. What will be its new radius (in $, mm$)?

When a wire of length $10 \ m$ is subjected to a force of $100 \ N$ along its length, the lateral strain produced is $0.01 \times 10^{-3} \ m$. The Poisson's ratio was found to be $0.4$. If the area of cross-section of the wire is $0.025 \ m^2$, its Young's modulus is:

$A$ metal wire having Poisson's ratio $1/4$ and Young's modulus $8 \times 10^{10} \, N/m^2$ is stretched by a force,which produces a lateral strain of $0.02 \%$ in it. The elastic potential energy stored per unit volume in the wire is [in $J/m^3$]

For silver,Young's modulus is $7.25 \times 10^{10} \ N/m^2$ and Bulk modulus is $11 \times 10^{10} \ N/m^2$. Its Poisson's ratio will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module