A wire is stretched 1 mm by a force F. If a | vedclass

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

Question

(D) The formula for Young's modulus $Y$ is given by $Y = \frac{F \cdot L}{A \cdot \Delta L}$,where $F$ is the force,$L$ is the length,$A$ is the cross

Vedclass · Accepted Answer

$\frac{1}{16} \ mm$

Vedclass · Answer

(D) The formula for Young's modulus $Y$ is given by $Y = \frac{F \cdot L}{A \cdot \Delta L}$,where $F$ is the force,$L$ is the length,$A$ is the cross-sectional area,and $\Delta L$ is the elongation.Since $A = \pi r^2 = \pi (d/2)^2 = \frac{\pi d^2}{4}$,we can write $\Delta L = \frac{F \cdot L}{Y \cdot A} = \frac{4 \cdot F \cdot L}{Y \cdot \pi d^2}$.Given that $F$,$L$,and $Y$ are constant for both wires,we have $\Delta L \propto \frac{1}{d^2}$.Let $\Delta L_1 = 1 \ mm$ and $d_1 = d$. For the second wire,$d_2 = 4d$.Therefore,$\frac{\Delta L_2}{\Delta L_1} = \left( \frac{d_1}{d_2} \right)^2 = \left( \frac{d}{4d} \right)^2 = \left( \frac{1}{4} \right)^2 = \frac{1}{16}$.Thus,$\Delta L_2 = \frac{1}{16} \cdot \Delta L_1 = \frac{1}{16} \cdot 1 \ mm = \frac{1}{16} \ mm$.

$A$ 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

Similar Questions

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

The correct increasing order for the modulus of elasticity for copper,steel,glass,and rubber is:

The length of a wire becomes $l_1$ and $l_2$ when $100\,N$ and $120\,N$ tensions are applied respectively. If $10l_2 = 11l_1$,the natural length of the wire will be $\frac{1}{x} l_1$. Here,the value of $x$ is ........

An Indian rubber cord $L$ metre long and area of cross-section $A$ $m^2$ is suspended vertically. The density of rubber is $D$ $kg/m^3$ and Young's modulus of rubber is $E$ $N/m^2$. If the wire extends by $l$ metre under its own weight,then the extension $l$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module