A tension of 22 ~N is applied to a copper wir | vedclass

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

Question

(A) Given: Tension $F = 22 ~N$, Area $A = 0.02 ~cm^2 = 0.02 	imes 10^{-4} ~m^2$, Young's modulus $Y = 1.1 	imes 10^{11} ~N/m^2$, Poisson's ratio $\s

Vedclass · Accepted Answer

$1.28 	imes 10^{-6} ~cm^2$

Vedclass · Answer

(A) Given: Tension $F = 22 ~N$, Area $A = 0.02 ~cm^2 = 0.02 	imes 10^{-4} ~m^2$, Young's modulus $Y = 1.1 	imes 10^{11} ~N/m^2$, Poisson's ratio $\sigma = 0.32$.Longitudinal strain is given by $\frac{\Delta l}{l} = \frac{F}{AY} = \frac{22}{0.02 	imes 10^{-4} 	imes 1.1 	imes 10^{11}} = \frac{22}{2.2 	imes 10^5} = 10^{-4}$.Poisson's ratio is defined as $\sigma = - \frac{\Delta r/r}{\Delta l/l}$. The lateral strain is $\frac{\Delta r}{r} = -\sigma \frac{\Delta l}{l}$.The area $A = \pi r^2$, so $\frac{\Delta A}{A} = 2 \frac{\Delta r}{r}$.Substituting the lateral strain, $\frac{\Delta A}{A} = -2 \sigma \frac{\Delta l}{l}$.The magnitude of decrease in area is $\Delta A = 2 \sigma A \frac{\Delta l}{l}$.$\Delta A = 2 	imes 0.32 	imes 0.02 ~cm^2 	imes 10^{-4} = 0.64 	imes 0.02 	imes 10^{-4} ~cm^2 = 0.0128 	imes 10^{-4} ~cm^2 = 1.28 	imes 10^{-6} ~cm^2$.

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

Similar Questions

An animal phylum having radially symmetrical adults but bilateral symmetrical larvae is

When a horse pulls a wagon,the force that causes the horse to move forward is the force:

Which of the following organisms is not correctly matched with its taxonomic category?

Two particles having position vectors $r_1 = (3 \hat{i} + 5 \hat{j}) \ m$ and $r_2 = (-5 \hat{i} - 3 \hat{j}) \ m$ are moving with velocities $v_1 = (4 \hat{i} + 3 \hat{j}) \ m/s$ and $v_2 = (a \hat{i} + 7 \hat{j}) \ m/s$. If they collide after $2 \ s$,then the value of $a$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module