The following four wires of length L and radi | vedclass

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

Question

(A) The extension $e$ of a wire is given by the formula $e = \frac{FL}{AY}$,where $F$ is the applied force,$L$ is the length,$A$ is the cross-sectiona

Vedclass · Accepted Answer

$L=100 \ cm, r=0.2 \ mm$

Vedclass · Answer

(A) The extension $e$ of a wire is given by the formula $e = \frac{FL}{AY}$,where $F$ is the applied force,$L$ is the length,$A$ is the cross-sectional area,and $Y$ is Young's modulus.Since $A = \pi r^2$,we have $e = \frac{FL}{\pi r^2 Y}$.Given that $F$ and $Y$ are the same for all wires,the extension is proportional to the ratio $\frac{L}{r^2}$,i.e.,$e \propto \frac{L}{r^2}$.Let us calculate the value of $\frac{L}{r^2}$ for each case:For option $A$: $\frac{100}{(0.2)^2} = \frac{100}{0.04} = 2500$.For option $B$: $\frac{200}{(0.4)^2} = \frac{200}{0.16} = 1250$.For option $C$: $\frac{300}{(0.6)^2} = \frac{300}{0.36} \approx 833.3$.For option $D$: $\frac{400}{(0.8)^2} = \frac{400}{0.64} = 625$.Comparing these values,the wire in option $A$ has the largest value of $\frac{L}{r^2}$,and therefore,it will have the largest extension.

The following four wires of length $L$ and radius $r$ are made of the same material. Which of these will have the largest extension,when the same tension is applied?

Similar Questions

$A$ uniform plank of Young's modulus $Y$ is moved over a smooth horizontal surface by a constant horizontal force $F$. The area of cross-section of the plank is $A$. The compressive strain on the plank in the direction of the force is

For four wires made of the same material,if the same force is applied,in which wire will the increase in length be maximum?

Two wires $A$ and $B$ of the same length are made of the same material. The load $(F)$ vs. elongation $(x)$ graph for these two wires is shown in the figure. Which of the following statement$(s)$ is/are true?

What force is required to increase the length of a wire of diameter $4 \, mm$ and Young's modulus $9 \times 10^{10} \, N/m^2$ by $0.1\%$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module