A rigid bar of mass 15; kg is supported symme | vedclass

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

Question

(A) The tension force $F$ acting on each wire is the same. Since the wires are of the same length $L$,the extension $\Delta L$ in each case is the sam

Vedclass · Accepted Answer

Ratio of diameter of copper to iron wire is $1.31:1$

Vedclass · Answer

(A) The tension force $F$ acting on each wire is the same. Since the wires are of the same length $L$,the extension $\Delta L$ in each case is the same. Thus,the strain $\epsilon = \frac{\Delta L}{L}$ is the same for all wires.From the definition of Young's modulus $Y = \frac{	ext{Stress}}{	ext{Strain}} = \frac{F/A}{\epsilon}$,we have $A = \frac{F}{Y \epsilon}$.Since $F$ and $\epsilon$ are constant,$A \propto \frac{1}{Y}$.Given the area of a circular wire $A = \frac{\pi d^2}{4}$,we have $d^2 \propto \frac{1}{Y}$,or $d \propto \frac{1}{\sqrt{Y}}$.Therefore,the ratio of the diameter of the copper wire $(d_c)$ to the iron wire $(d_i)$ is $\frac{d_c}{d_i} = \sqrt{\frac{Y_i}{Y_c}}$.Given $Y_i = 190 	imes 10^9 \; Pa$ and $Y_c = 110 	imes 10^9 \; Pa$,we get:$\frac{d_c}{d_i} = \sqrt{\frac{190 	imes 10^9}{110 	imes 10^9}} = \sqrt{\frac{19}{11}} \approx 1.31$.Thus,the ratio of their diameters is $1.31:1$.

$A$ rigid bar of mass $15\; kg$ is supported symmetrically by three wires each $2.0\; m$ long. Those at each end are of copper and the middle one is of iron. Determine the ratio of their diameters if each is to have the same tension.

Similar Questions

If the length of a wire is made double and the radius is halved of its respective values,then the Young's modulus of the material of the wire will:

The modulus of elasticity is dimensionally equivalent to

Two similar wires under the same load yield elongations of $0.1 \ mm$ and $0.05 \ mm$ respectively. If the area of cross-section of the first wire is $4 \ mm^2$,then the area of cross-section of the second wire is..... $mm^2$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module