A copper wire of length 3 text{ m} is stretch | vedclass

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

Question

(A) The elastic potential energy $U$ stored in a stretched wire is given by the formula: $U = \frac{1}{2} 	imes 	ext{Stress} 	imes 	ext{Strain}

Vedclass · Accepted Answer

$33$

Vedclass · Answer

(A) The elastic potential energy $U$ stored in a stretched wire is given by the formula: $U = \frac{1}{2} 	imes 	ext{Stress} 	imes 	ext{Strain} 	imes 	ext{Volume}$.Since $	ext{Stress} = Y 	imes 	ext{Strain}$, we have $U = \frac{1}{2} 	imes Y 	imes (	ext{Strain})^2 	imes 	ext{Volume}$.Given:Length $L = 3 	ext{ m}$,Extension $\Delta L = 3 	ext{ mm} = 3 	imes 10^{-3} 	ext{ m}$,Volume $V = 600 	imes 10^{-6} 	ext{ m}^3$,Young's modulus $Y = 1.1 	imes 10^{11} 	ext{ N/m}^2$.Calculate Strain: $	ext{Strain} = \frac{\Delta L}{L} = \frac{3 	imes 10^{-3}}{3} = 10^{-3}$.Now, substitute the values into the formula:$U = \frac{1}{2} 	imes (1.1 	imes 10^{11}) 	imes (10^{-3})^2 	imes (600 	imes 10^{-6})$$U = 0.5 	imes 1.1 	imes 10^{11} 	imes 10^{-6} 	imes 600 	imes 10^{-6}$$U = 0.5 	imes 1.1 	imes 600 	imes 10^{-1}$$U = 0.5 	imes 1.1 	imes 60 = 33 	ext{ J}$.

Similar Questions

If $S$ is stress and $Y$ is Young's modulus of the material of a wire,the energy stored in the wire per unit volume is

When a weight $Mg$ is suspended from a wire of length $L$,the increase in length is $l$ meters. The energy stored in the wire is:

Which of the following is true for elastic potential energy density?

Two wires $A$ and $B$ having same length and material are stretched by the same force. Their diameters are in the ratio $1: 3$. The ratio of energy density of wire $A$ to that of wire $B$ when stretched,is (in $: 1$)

$A$ wire of length $25 \ cm$ and radius $2 \ mm$ is fixed at one end. If a torque is applied at the other end to produce an angular displacement of $45^o$,calculate the work done in $J$. (Given: $\eta = 8 \times 10^{10} \ N/m^2$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module