A material has Poisson's ratio 0.5. If a unif | vedclass

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

Question

(D) The Poisson's ratio $\sigma$ is defined as the ratio of lateral strain to longitudinal strain: $\sigma = -\frac{\Delta r/r}{\Delta l/l} = 0.5$.Giv

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(D) The Poisson's ratio $\sigma$ is defined as the ratio of lateral strain to longitudinal strain: $\sigma = -\frac{\Delta r/r}{\Delta l/l} = 0.5$.Given longitudinal strain $\frac{\Delta l}{l} = 3 	imes 10^{-3}$.Therefore, lateral strain $\frac{\Delta r}{r} = -\sigma 	imes \frac{\Delta l}{l} = -0.5 	imes 3 	imes 10^{-3} = -1.5 	imes 10^{-3}$.The volume of a cylindrical rod is $V = \pi r^2 l$.Taking the logarithmic derivative, the fractional change in volume is $\frac{\Delta V}{V} = 2\frac{\Delta r}{r} + \frac{\Delta l}{l}$.Substituting the values: $\frac{\Delta V}{V} = 2(-1.5 	imes 10^{-3}) + (3 	imes 10^{-3}) = -3 	imes 10^{-3} + 3 	imes 10^{-3} = 0$.Thus, the percentage increase in volume is $0\%$.

$A$ material has Poisson's ratio $0.5$. If a uniform rod of it suffers a longitudinal strain of $3 \times 10^{-3}$, what will be the percentage increase in volume? .......... $\%$

Similar Questions

If there is no change in the volume of a wire upon stretching,then the Poisson's ratio for the material of the wire is:

$A$ 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:

The stress along the length of a rod (with rectangular cross-section) is $1 \%$ of the Young's modulus of its material. What is the approximate percentage of change of its volume (in $\%$)? (Poisson's ratio of the material of the rod is $0.3$.)

The minimum and maximum values of Poisson's ratio for a metal lie between

There is no change in the volume of a wire due to change in its length on stretching. The Poisson's ratio of the material of the wire is

Vedclass Test Series

Exam Paper Generator

Online Exam Module