A uniform heavy rod of weight $10\, {kg} {ms}^{-2}$, crosssectional area $100\, {cm}^{2}$ and length $20\, {cm}$ is hanging from a fixed support. Young modulus of the material of the rod is $2 \times 10^{11} \,{Nm}^{-2}$. Neglecting the lateral contraction, find the elongation of rod due to its own weight. (In $\times 10^{-10} {m}$)
JEE MAIN 2021, Diffcult
Download our app for free and get started
We know,
$\Delta \ell=\frac{{WL}}{2 {AY}}$
$\Delta \ell=\frac{10 \times 1}{2 \times 5} \times 100 \times 10^{-4} \times 2 \times 10^{11}$
$\Delta \ell=\frac{1}{2} \times 10^{-9}=5 \times 10^{-10}\, {m}$
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
- 1The strain energy stored in a body of volume $V$ due to shear strain $\phi$ is (shear modulus is $\eta$ )View Solution
- 2A spherical ball contracts in volume by $0.02 \%$, when subjected to a normal uniform pressure of $50$ atmosphere. The Bulk modulus of its material is ............. $Nm ^{-2}$View Solution
- 3Two wires of the same material have lengths in the ratio 1 : 2 and their radii are in the ratio $1:\sqrt 2 $. If they are stretched by applying equal forces, the increase in their lengths will be in the ratioView Solution
- 4In a wire of length $L,$ the increase in its length is $l.$ If the length is reduced to half, the increase in its length will beView Solution
- 5A steel rod of length $\ell$, cross sectional area $A$, young's modulus of elasticity $Y$, and thermal coefficient of linear expansion $'a'$ is heated so that its temperature increases by $t\,^oC$. Work that can be done by rod on heating will beView Solution
- 6View SolutionThe longitudinal strain is only possible in
- 7A rod is fixed between two points at $20°C$. The coefficient of linear expansion of material of rod is $1.1 \times {10^{ - 5}}/^\circ C$ and Young's modulus is $1.2 \times {10^{11}}\,N/m$. Find the stress developed in the rod if temperature of rod becomes $10°C$View Solution
- 8A rod of length $l$ and area of cross-section $A$ is heated from $0°C$ to $100°C$. The rod is so placed that it is not allowed to increase in length, then the force developed is proportional toView Solution
- 9The 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
- 10The diameter of a brass rod is 4 mm and Young's modulus of brass is $9 \times {10^{10}}\,N/{m^2}$. The force required to stretch by $0.1\%$ of its length isView Solution