A wire of initial length L and radius r is st | vedclass

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

Question

(D) The elastic potential energy per unit volume $(u)$ of a stretched wire is given by the formula: $u = \frac{1}{2} 	imes Y 	imes (	ext{strain})^2

Vedclass · Accepted Answer

$1: 1$

Vedclass · Answer

(D) The elastic potential energy per unit volume $(u)$ of a stretched wire is given by the formula: $u = \frac{1}{2} 	imes Y 	imes (	ext{strain})^2$, where $Y$ is Young's modulus and $	ext{strain} = \frac{\Delta L}{L}$.For the first wire: $	ext{strain}_1 = \frac{l}{L}$.Thus, $u_1 = \frac{1}{2} Y (\frac{l}{L})^2$.For the second wire: $	ext{strain}_2 = \frac{2l}{2L} = \frac{l}{L}$.Thus, $u_2 = \frac{1}{2} Y (\frac{l}{L})^2$.Since both wires are made of the same material, their Young's modulus $Y$ is the same.The ratio of the stored elastic energy per unit volume is $\frac{u_1}{u_2} = \frac{\frac{1}{2} Y (l/L)^2}{\frac{1}{2} Y (l/L)^2} = 1:1$.

$A$ wire of initial length $L$ and radius $r$ is stretched by a length $l$. Another wire of same material but with initial length $2L$ and radius $2r$ is stretched by a length $2l$. The ratio of stored elastic energy per unit volume in the first and second wire is

Similar Questions

What is called elastic energy density? Write its formula and dimensional formula.

$A$ wire suspended vertically from one end is stretched by attaching a weight $200 \,N$ to the lower end. The weight stretches the wire by $1 \,mm$. The elastic potential energy gained by the wire is ....... $J$

$A$ wire of Young's modulus $1.6 \times 10^{12} \,N/m^{2}$ is stretched by a force so as to produce a strain of $2 \times 10^{-4}$. The energy density of the wire is

Which of the following wires has the maximum elastic potential energy?

Two wires of the same material and length but diameters in the ratio $1:2$ are stretched by the same force. The elastic potential energy per unit volume for the wires,when stretched by the same force,will be in the ratio: (in $:1$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module