An aluminium rod with Young's modulus $Y =7.0$ $\times 10^{10} N / m ^2$ undergoes elastic strain of $0.04 \%$. The energy per unit volume stored in the rod in SI unit is:
JEE MAIN 2023, Easy
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
- 1Two blocks of mass $2 \mathrm{~kg}$ and $4 \mathrm{~kg}$ are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is $4.0 \times 10^{-5}$ $\mathrm{m}$ and Young's modulus of the metal is $2.0 \times 10^{11} \mathrm{~N} / \mathrm{m}^2$. The longitudinal strain developed in the wire is $\frac{1}{\alpha \pi}$. The value of $\alpha$ is [Use $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )View Solution
- 2A $0.1 \mathrm{~kg}$ mass is suspended from a wire of negligible mass. The length of the wire is $1 \mathrm{~m}$ and its crosssectional area is $4.9 \times 10^{-7} \mathrm{~m}^2$. If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency $140 \ \mathrm{rad} \mathrm{s}^{-1}$. If the Young's modulus of the material of the wire is $\mathrm{n} \times 10^9 \mathrm{Nm}^{-2}$, the value of $\mathrm{n}$ isView Solution
- 3The upper end of a wire of diameter $12\,mm$ and length $1\,m$ is clamped and its other end is twisted through an angle of $30^{\circ}$. The angle of shear is$........^{\circ}$View Solution
- 4A metal block of mass $m$ is suspended from a rigid support through a metal wire of diameter $14\,mm$. The tensile stress developed in the wire under equilibrium state is $7 \times 10^5\,Nm ^{-2}$. The value of mass $m$ is $......kg$.View Solution
(Take, $g =9.8\,ms ^{-2}$ and $\left.\pi=\frac{22}{7}\right)$
- 5The specific heat at constant pressure and at constant volume for an ideal gas are ${C_p}$ and ${C_v}$ and its adiabatic and isothermal elasticities are ${E_\varphi }$ and ${E_\theta }$ respectively. The ratio of ${E_\varphi }$ to ${E_\theta }$ isView Solution
- 6A wire of length $50\, cm$ and cross sectional area of $1$ sq. mm is extended by $1\, mm.$ The required work will be $(Y = 2 \times {10^{10}}\,N{m^{ - 2}})$View Solution
- 7If the Bulk modulus of lead is $8.0 \times 10^9 \,N / m ^2$ and the initial density of the lead is $11.4 \,g / cc$, then under the pressure of $2.0 \times 10^8 \,N / m ^2$, the density of the lead is ............. $g / cc$View Solution
- 8A copper wire of length $1.0\, m$ and a steel wire of length $0.5\, m$ having equal cross-sectional areas are joined end to end. The composite wire is stretched by a certain load which stretches the copper wire by $1\, mm$. If the Young's modulii of copper and steel are respectively $1.0\times10^{11}\, Nm^{-2}$ and $2.0\times10^{11}\, Nm^{- 2}$, the total extension of the composite wire is ........ $mm$View Solution
- 9The density and breaking stress of a wire are $6 \times$ $10^4 \mathrm{~kg} / \mathrm{m}^3$ and $1.2 \times 10^8 \mathrm{~N} / \mathrm{m}^2$ respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is $\frac{1^{\text {rd }}}{3}$ of the value on the surface of earth. The maximum length of the wire with breaking is ............ $\mathrm{m}$ (take, $\mathrm{g}=$ $\left.10 \mathrm{~m} / \mathrm{s}^2\right)$View Solution
- 10View SolutionStress to strain ratio is equivalent to