A steel and a brass wire, each of length 50 , | vedclass

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

Question

(B) Let $Y_s$ and $Y_b$ be the Young's modulus of steel and brass respectively. Given $Y_s = 2 	imes 10^{12} \,dynes/cm^{2}$ and $Y_b = 1 	imes 10^{

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(B) Let $Y_s$ and $Y_b$ be the Young's modulus of steel and brass respectively. Given $Y_s = 2 	imes 10^{12} \,dynes/cm^{2}$ and $Y_b = 1 	imes 10^{12} \,dynes/cm^{2}$.Let $L = 50 \,cm$ be the length, $A = 0.005 \,cm^{2}$ be the cross-sectional area, and $\Delta L = 0.1 \,cm$ be the extension for both wires.The tension $T$ in a wire is given by $T = \frac{Y A \Delta L}{L}$.Since $A, \Delta L,$ and $L$ are the same for both wires, the tension $T$ is directly proportional to the Young's modulus $Y$ $(T \propto Y)$.Let $T_s$ be the tension in the steel wire and $T_b$ be the tension in the brass wire.$T_s = \frac{Y_s A \Delta L}{L}$ and $T_b = \frac{Y_b A \Delta L}{L}$.Taking torque about the point where the load $W$ is applied at a distance $x$ from the steel wire:$T_s \cdot x = T_b \cdot (15 - x)$.Substituting the proportionality $T_s \propto Y_s$ and $T_b \propto Y_b$:$Y_s \cdot x = Y_b \cdot (15 - x)$.$(2 	imes 10^{12}) \cdot x = (1 	imes 10^{12}) \cdot (15 - x)$.$2x = 15 - x$.$3x = 15$.$x = 5 \,cm$.

Similar Questions

The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?

$A$ bar is subjected to axial forces as shown. If $E$ is the modulus of elasticity of the bar and $A$ is its cross-section area,its total elongation will be:

Two different wires made with the same material have their radii in the ratio $1:2$. Their lengths are also in the ratio $1:2$. If the extensions produced are equal when subjected to different loads,find the ratio of the loads applied.

$A$ steel rod of diameter $1\,cm$ is clamped firmly at each end when its temperature is $25\,^{\circ}C$ so that it cannot contract on cooling. The tension in the rod at $0\,^{\circ}C$ is approximately ......... $N$ $(\alpha = 10^{-5}/\,^{\circ}C, Y = 2 \times 10^{11}\,N/m^2)$

Vedclass Test Series

Exam Paper Generator

Online Exam Module