The area of a cross-section of steel wire is $0.1\,\,cm^2$ and Young's modulus of steel is $2\,\times \,10^{11}\,\,N\,\,m^{-2}.$ The force required to stretch by $0.1\%$ of its length is ......... $N$.
Medium
Download our app for free and get started
Here,
$A=0.1 \mathrm{cm}^{2}=0.1 \times 10^{-4} \mathrm{m}^{2}$
$Y=2 \times 10^{11} \mathrm{N} / \mathrm{m}^{-2}$
$\frac{\Delta \mathrm{L}}{\mathrm{L}}=0.1 \%=\frac{0.1}{100}=0.1 \times 10^{-2}$
$\mathrm{As} \mathrm{Y}=\frac{\mathrm{F} / \mathrm{A}}{\Delta \mathrm{L} / \mathrm{L}}$
$\therefore \quad F=Y \frac{\Delta L}{L} A$
$=2 \times 10^{11} \mathrm{Nm}^{-2} \times 0.1 \times 10^{-2} \times 0.1 \times 10^{-4} \mathrm{m}^{2}$
$=2 \times 10^{3} \mathrm{N}=2000 \mathrm{N}$
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
- 1View SolutionWhy the spring is made up of steel in comparison of copper
- 2A steel plate of face area $1 \,cm ^2$ and thickness $4 \,cm$ is fixed rigidly at the lower surface. A tangential force $F=10 \,kN$ is applied on the upper surface as shown in the figure. The lateral displacement $x$ of upper surface w.r.t. the lower surface is .............. $m$ (Modulus of rigidity for steel is $8 \times 10^{11} \,N / m ^2$ )View Solution
- 3View SolutionWhich of the following affects the elasticity of a substance
- 4Two wires of same diameter of the same material having the length $l$ and $2l.$ If the force $ F$ is applied on each, the ratio of the work done in the two wires will beView Solution
- 5View SolutionA stretched rubber has
- 6Rod of constant cross-section moves towards right with constant acceleration. Graph of stress and distance from left end is given as in figure. If density of material of rod at cross section $1$ is $9$ $\frac{{gm}}{{c{m^3}}}$ . Find density at cross section $2$.View Solution
.......... $\mathrm{gm} / \mathrm{cm}^{3}$
- 7A wire elongates by $l$ $mm$ when a load $W$ is hanged from it. If the wire goes over a pulley and two weights $W$ each are hung at the two ends, the elongation of the wire will be (in $mm$)View Solution
- 8View SolutionThe isothermal bulk modulus of a gas at atmospheric pressure is
- 9When a load of $10 \,kg$ is suspended on a metallic wire, its length increase by $2 \,mm$. The force constant of the wire is $....... N / m$View Solution
- 10$Assertion :$ Solids are least compressible and gases are most compressible.View Solution
$Reason :$ solids have definite shape and volume but gases do not have either definite shape or definite volume.