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

Which coefficient of elasticity is responsible for the propagation of a wave in a string?

$A$ uniform rod of mass $m$,length $L$,area of cross-section $A$ and Young's modulus $Y$ hangs from the ceiling. Its elongation under its own weight will be

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?

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