The following four wires are made of the same | vedclass

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

Question

(D) The formula for elongation $\Delta L$ is given by $\Delta L = \frac{FL}{AY}$,where $F$ is the tension,$L$ is the length,$A$ is the cross-sectional

Vedclass · Accepted Answer

Length $400 \, cm$,diameter $0.01 \, mm$

Vedclass · Answer

(D) The formula for elongation $\Delta L$ is given by $\Delta L = \frac{FL}{AY}$,where $F$ is the tension,$L$ is the length,$A$ is the cross-sectional area,and $Y$ is Young's modulus.Since all wires are made of the same material,$Y$ is constant. For the same tension $F$,the elongation $\Delta L \propto \frac{L}{A}$.Since $A = \pi r^2 = \pi (d/2)^2 = \frac{\pi d^2}{4}$,we have $\Delta L \propto \frac{L}{d^2}$.Calculating the ratio $L/d^2$ for each option:$A: \frac{500}{(0.05)^2} = \frac{500}{0.0025} = 200,000$$B: \frac{200}{(0.02)^2} = \frac{200}{0.0004} = 500,000$$C: \frac{300}{(0.03)^2} = \frac{300}{0.0009} \approx 333,333$$D: \frac{400}{(0.01)^2} = \frac{400}{0.0001} = 4,000,000$Comparing the values,option $D$ has the largest ratio,hence it will have the largest elongation.

The following four wires are made of the same material. Which one will have the largest elongation when subjected to the same tension?

Similar Questions

$A$ wire is stretched $1 \ mm$ by a force $F$. If a second wire of same material,same length and $4$ times the diameter of the first wire is stretched by the same force $F$,then the elongation of the second wire is

What is bending? How can bending problems be prevented,and what is buckling?

How much force is required to produce an increase of $0.2\%$ in the length of a brass wire of diameter $0.6\, mm$ (Young's modulus for brass = $0.9 \times 10^{11} \, N/m^2$)?

The length of an iron wire is $L$ and the area of cross-section is $A$. The increase in length is $l$ upon applying a force $F$ on its two ends. Which of the following statements is correct?

Vedclass Test Series

Exam Paper Generator

Online Exam Module