Two wires A and B of the same length are made | vedclass

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

Question

(A, D) Since both wires are made of the same material,their Young's modulus $(Y)$ is identical.Young's modulus is given by $Y = \frac{F L}{A x}$,where

Vedclass · Accepted Answer

Young's modulus of both $A$ and $B$ are the same.

Vedclass · Answer

(A, D) Since both wires are made of the same material,their Young's modulus $(Y)$ is identical.Young's modulus is given by $Y = \frac{F L}{A x}$,where $F$ is the load,$L$ is the length,$A$ is the cross-sectional area,and $x$ is the elongation.Rearranging for the load,we get $F = (\frac{Y A}{L}) x$.Since $Y$ and $L$ are the same for both wires,the slope of the $F-x$ graph is proportional to the cross-sectional area $A$ (i.e.,$	ext{slope} = \frac{Y A}{L} \propto A$).From the graph,the slope of line $A$ is greater than the slope of line $B$,which implies that the cross-sectional area of $A$ is greater than that of $B$ $(A_A > A_B)$.Therefore,statement $A$ is true and statement $D$ is true.

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?

Similar Questions

Steel and copper wires of the same length are stretched by the same weight one after the other. The Young's modulus of steel and copper are $2 \times 10^{11} \, N/m^2$ and $1.2 \times 10^{11} \, N/m^2$,respectively. What is the ratio of the increase in their lengths?

The maximum elongation of a steel wire of $1 \,m$ length if the elastic limit of steel and its Young's modulus,respectively,are $8 \times 10^8 \,N \,m^{-2}$ and $2 \times 10^{11} \,N \,m^{-2}$,is: (in $\,mm$)

Three bars having lengths $l, 2l$,and $3l$ and areas of cross-section $A, 2A$,and $3A$ are joined rigidly end to end. The compound rod is subjected to a stretching force $F$. The total increase in the length of the rod is (Young's modulus of the material is $Y$ and the bars are massless).

Vedclass Test Series

Exam Paper Generator

Online Exam Module