When a wire of length 10 m is subjected to a | vedclass

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

Question

(A) Poisson's ratio $(\sigma) = \frac{	ext{lateral strain}}{	ext{longitudinal strain}}$.Given lateral strain $= 0.01 	imes 10^{-3} \ m$ (Note: Stra

Vedclass · Accepted Answer

$1.6 	imes 10^8 \ N/m^2$

Vedclass · Answer

(A) Poisson's ratio $(\sigma) = \frac{	ext{lateral strain}}{	ext{longitudinal strain}}$.Given lateral strain $= 0.01 	imes 10^{-3} \ m$ (Note: Strain is dimensionless,assuming the value represents the change in diameter $\Delta D$ or similar,but here we use it directly as the numerator for the ratio).$\sigma = \frac{	ext{lateral strain}}{\Delta L / L} = 0.4$.$\frac{\Delta L}{L} = \frac{0.01 	imes 10^{-3}}{0.4} = 0.025 	imes 10^{-3} = 2.5 	imes 10^{-5}$.Young's modulus $Y = \frac{F/A}{\Delta L/L} = \frac{F \cdot L}{A \cdot \Delta L}$.$Y = \frac{100 \ N}{0.025 \ m^2 	imes (2.5 	imes 10^{-5})} = \frac{100}{0.0625 	imes 10^{-5}} = \frac{100}{6.25 	imes 10^{-7}} = 16 	imes 10^7 = 1.6 	imes 10^8 \ N/m^2$.

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:

Similar Questions

Choose the correct relationship between Poisson's ratio $(\sigma)$,bulk modulus $(K)$,and modulus of rigidity $(\eta)$ of a given solid object:

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

For a homogeneous isotropic material, which one of the following cannot be the value of Poisson’s ratio?

$A$ 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 $J/m^3$]

The value of Poisson's ratio lies between

Vedclass Test Series

Exam Paper Generator

Online Exam Module