On all the six surfaces of a unit cube,an equ | vedclass

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

Question

(C) For a unit cube (side length $L = 1$),the tensile stress on each face is $\sigma_{stress} = \frac{F}{A} = \frac{F}{1^2} = F$.The longitudinal stra

Vedclass · Accepted Answer

$\frac{F(1 - 2\sigma)}{Y}$

Vedclass · Answer

(C) For a unit cube (side length $L = 1$),the tensile stress on each face is $\sigma_{stress} = \frac{F}{A} = \frac{F}{1^2} = F$.The longitudinal strain along one axis due to the force on that axis is $\epsilon_{long} = \frac{F}{Y}$.Due to the tensile forces on the other two perpendicular faces,there will be lateral strains. The lateral strain due to one perpendicular force is $-\sigma \epsilon_{long} = -\sigma \frac{F}{Y}$.Since there are two such perpendicular faces,the total lateral strain is $2 	imes (-\sigma \frac{F}{Y}) = -\frac{2\sigma F}{Y}$.The net strain (change in length $\Delta L$ for $L=1$) is the sum of the longitudinal strain and the lateral strains:$\Delta L = \frac{F}{Y} - \frac{2\sigma F}{Y} = \frac{F(1 - 2\sigma)}{Y}$.

On all the six surfaces of a unit cube,an equal tensile force of $F$ is applied. The increase in length of each side will be ($Y =$ Young's modulus,$\sigma =$ Poisson's ratio).

Similar Questions

$A$ wire of length $L$ and radius $r$ is loaded with a weight $Mg$. If $Y$ and $\sigma$ denote the Young's modulus and Poisson's ratio of the material of the wire respectively,then the decrease in the radius of the wire $(\Delta r)$ is given by:

$A$ copper wire of cross-sectional area $0.01 \,cm^2$ is under a tension of $22 \,N$. The decrease in the cross-sectional area is (Young modulus $= 1.1 \times 10^{11} \,N/m^2$, Poisson's ratio $= 0.32$)

$A$ tension of $22 \,N$ is applied to a copper wire of cross-sectional area $0.02 \,cm^2$. Young's modulus of copper is $1.1 \times 10^{11} \,N/m^2$ and Poisson's ratio is $0.32$. The decrease in cross-sectional area will be:

Which of the following relations is true for the elastic moduli of a material?

In materials like aluminium and copper, the correct order of magnitude of various elastic moduli is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module