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 $5 \times 10^{-4}$.
JEE MAIN 2022, Medium
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A brass rod of cross-sectional area $1\,c{m^2}$ and length $0.2\, m$ is compressed lengthwise by a weight of $5\, kg$. If Young's modulus of elasticity of brass is $1 \times {10^{11}}\,N/{m^2}$ and $g = 10\,m/{\sec ^2}$, then increase in the energy of the rod will beView Solution
- 2A steel rod is projecting out of rigid wall. The shearing strength of steel is $345 \,\,MN/m^2.$ The dimensions $AB = 5\,\, cm,\,BC = BE = 2\,\, cm.$ The maximum load that can be put on the face $ABCD$ is .......... $kg$ (neglect bending of the rod) $(g = 10\,\, m/s^2)$View Solution
- 3The stress versus strain graphs for wires of two materials $A$ and $B$ are as shown in the figure. If ${Y_A}$ and ${Y_B}$ are the Young ‘s modulii of the materials, thenView Solution
- 4A metal rod of cross-sectional area $10^{-4} \,m ^{2}$ is hanging in a chamber kept at $20^{\circ} C$ with a weight attached to its free end. The coefficient of thermal expansion of the rod is $2.5 \times 10^{-6} \,K ^{-1}$ and its Young's modulus is $4 \times 10^{12} \,N / m ^{2}$. When the temperature of the chamber is lowered to $T$, then a weight of $5000 \,N$ needs to be attached to the rod, so that its length is unchanged. Then, $T$ is ............ $^{\circ} C$View Solution
- 5A steel wire of diameter $2\ mm$ has a breaking strength of $4 \times 10^5 N$.the breaking force $......... \times 10^5 N$ of similar steel wire of diameter $1.5\ mm ?$View Solution
- 6Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is $1: 4,$ the ratio of their diameters isView Solution
- 7A force of $200\, N$ is applied at one end of a wire of length $2\, m$ and having area of cross-section ${10^{ - 2}}\,c{m^2}$. The other end of the wire is rigidly fixed. If coefficient of linear expansion of the wire $\alpha = 8 \times 10{^{-6}}°C^{-1}$ and Young's modulus $Y = 2.2 \times {10^{11}}\,N/{m^2}$ and its temperature is increased by $5°C$, then the increase in the tension of the wire will be ........ $N$View Solution
- 8The diagram shows stress v/s strain curve for the materials $A$ and $B$. From the curves we infer thatView Solution
- 9A horizontal steel railroad track has a length of $100 \,m$, when the temperature is $25^{\circ} C$. The track is constrained from expanding or bending. The stress on the track on a hot summer day, when the temperature is $40^{\circ} C$ is ............. $\times 10^7\,Pa$ (Note : The linear coefficient of thermal expansion for steel is $1.1 \times 10^{-5} /{ }^{\circ} C$ and the Young's modulus of steel is $2 \times 10^{11} \,Pa$ )View Solution
- 10A uniform wire of length $L$ and radius $r$ is twisted by an angle $\alpha$. If modulus of rigidity of the wire is $\eta,$ then the elastic potential energy stored in wire, is $.........$View Solution