The Young's modulus of a steel wire of length | vedclass

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

Question

(C) Given:Length $L = 6\,m$Area $A = 3\,mm^2 = 3 	imes 10^{-6}\,m^2$Young's modulus $Y = 2 	imes 10^{11}\,N/m^2$Mass $m = 4\,kg$Gravity on Earth $g_

Vedclass · Accepted Answer

$0.1\,mm$

Vedclass · Answer

(C) Given:Length $L = 6\,m$Area $A = 3\,mm^2 = 3 	imes 10^{-6}\,m^2$Young's modulus $Y = 2 	imes 10^{11}\,N/m^2$Mass $m = 4\,kg$Gravity on Earth $g_e = 10\,m/s^2$Gravity on planet $g_p = \frac{1}{4} g_e = \frac{10}{4} = 2.5\,m/s^2$The tension $F$ in the wire is equal to the weight of the block on the planet:$F = m 	imes g_p = 4 	imes 2.5 = 10\,N$The formula for elongation $\Delta L$ is:$\Delta L = \frac{FL}{AY}$Substituting the values:$\Delta L = \frac{10 	imes 6}{3 	imes 10^{-6} 	imes 2 	imes 10^{11}}$$\Delta L = \frac{60}{6 	imes 10^5} = 10 	imes 10^{-5} = 10^{-4}\,m$Converting to millimeters:$\Delta L = 10^{-4} 	imes 10^3\,mm = 0.1\,mm$

Similar Questions

$A$ wire elongates by $l \ mm$ when a load $W$ is hanged from it. If the wire goes over a pulley and two weights $W$ each are hung at the two ends,the elongation of the wire will be (in $mm$)

The speed of a transverse wave travelling in a wire of length $50 \text{ cm}$,cross-sectional area $1 \text{ mm}^2$ and mass $5 \text{ g}$ is $80 \text{ ms}^{-1}$. The Young's modulus of the material of the wire is $4 \times 10^{11} \text{ Nm}^{-2}$. The extension in the length of the wire is

If the ratio of lengths,radii,and Young's moduli of steel and brass wires in the figure are $a, b,$ and $c$ respectively,then the corresponding ratio of increase in their lengths is

Two wires $A$ and $B$ are made of the same material having a ratio of lengths $\frac{L_A}{L_B} = \frac{1}{3}$ and their diameters ratio $\frac{d_A}{d_B} = 2$. If both the wires are stretched using the same force,what would be the ratio of their respective elongations?

The decrease in length of a metal bar of length $L$ and cross-sectional area $A$ when compressed with a load $F$ along its length is (where $Y$ is Young's modulus of the material of the metal bar).

Vedclass Test Series

Exam Paper Generator

Online Exam Module