Elastic behaviour of material for linear streass and linear strain, is shown in figure. energy densi

English

Gujarati

Hindi

8.Mechanical Properties of Solids

medium

The elastic behaviour of material for linear streass and linear strain, is shown in the figure. The energy density for a linear strain of $5 \times 10^{-4}$ is $\dots \; kJ / m ^{3}$. Assume that material is elastic upto the linear strain of $5 \times 10^{-4}$.

A

$35$

B

$-35$

C

$25$

D

$-25$

(JEE MAIN-2022)

Solution

$y =\frac{\text { stress }}{\text { strain }}=2.0 \times 10^{10}$

Energy density $=\frac{1}{2} \; stress \; \times \; strain$

$=\frac{1}{2}(\text { strain })^{2} y =\frac{1}{2}\left(5 \times 10^{-4}\right)^{2} \times 20 \times 10^{10}$

$=25 \times 10^{2} \times 10=25 \frac{ kJ }{ m ^{3}}$

Ans. $25$

Standard 11

Physics

Share

Similar Questions

If the potential energy of a spring is $V$ on stretching it by $2\, cm$, then its potential energy when it is stretched by $10 \,cm$ will be

medium

When a $4\, kg$ mass is hung vertically on a light spring that obeys Hooke's law, the spring stretches by $2\, cms$. The work required to be done by an external agent in stretching this spring by $5\, cms$ will be ……… $joule$ $(g = 9.8\,metres/se{c^2})$

medium

Two wires of the same material (Young's modulus $Y$ ) and same length $L$ but radii $R$ and $2R$ respectively are joined end to end and a weight $W$ is suspended from the combination as shown in the figure. The elastic potential energy in the system is

hard

A wire of length $50\, cm$ and cross sectional area of $1$ sq. mm is extended by $1\, mm.$ The required work will be $(Y = 2 \times {10^{10}}\,N{m^{ – 2}})$

medium

An Indian rubber cord $L$ metre long and area of cross-section $A$ $metr{e^2}$ is suspended vertically. Density of rubber is $D$ $kg/metr{e^3}$ and Young's modulus of rubber is $E$ $newton/metr{e^2}$. If the wire extends by $l$ metre under its own weight, then extension $l$ is

hard