Two exactly similar wires of steel and copper are stretched by equal forces. If the total elongation is $2 \ cm$, then how much is the elongation in steel and copper wire respectively? Given, $Y_{\text {steel }}=20 \times 10^{11} dyne / \ cm ^2, Y_{\text {copper }}=12 \times 10^{11} dyne / \ cm ^2$
Medium
Download our app for free and get started
Let us say that elongation in copper $=x$
Than elongation in steel $=2-x$
We know
$\frac{F L}{A Y}=\Delta x$
$\because F, A, L$ are same only material is different We can say
$\frac{1}{Y} \propto \Delta x$
$\frac{Y_2}{Y_1}=\frac{\Delta x_1}{\Delta x_2}$ $\left\{\begin{array}{l}\text { Where } \\ Y_2=Y_{\text {steel }} \\ Y_1=Y_{\text {copper }} \\ \Delta x_1=\text { elongation in copper }=x \\ \Delta x_2=2-x\end{array}\right.$
Substituting values
$\frac{20 \times 10^{11}}{12 \times 10^{11}}=\frac{x}{2-x}$
$x=1.25 \ cm$
So $\Delta x_{\text {copper }}=1.25 \ cm $
$\Delta x_{\text {sleel }}=0.75 \ cm$
Than elongation in steel $=2-x$
We know
$\frac{F L}{A Y}=\Delta x$
$\because F, A, L$ are same only material is different We can say
$\frac{1}{Y} \propto \Delta x$
$\frac{Y_2}{Y_1}=\frac{\Delta x_1}{\Delta x_2}$ $\left\{\begin{array}{l}\text { Where } \\ Y_2=Y_{\text {steel }} \\ Y_1=Y_{\text {copper }} \\ \Delta x_1=\text { elongation in copper }=x \\ \Delta x_2=2-x\end{array}\right.$
Substituting values
$\frac{20 \times 10^{11}}{12 \times 10^{11}}=\frac{x}{2-x}$
$x=1.25 \ cm$
So $\Delta x_{\text {copper }}=1.25 \ cm $
$\Delta x_{\text {sleel }}=0.75 \ cm$
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 SolutionCorrect pair is ..........
- 2A rubber cord $10\, m$ long is suspended vertically. How much does it stretch under its own weight $($Density of rubber is $1500\, kg/m^3, Y = 5×10^8 N/m^2, g = 10 m/s^2$$)$View Solution
- 3View SolutionWhich one of the following quantities does not have the unit of force per unit area
- 4When a load $W$ is hung from a wire of length $2\ L$ , it just breaks. Now this wire is completely melted and a new wire of length $L$ is formed. If the load $W$ is hung from this new wireView Solution
- 5View SolutionIn materials like aluminium and copper, the correct order of magnitude of various elastic modulii is
- 6In an experiment to determine the Young's modulus, steel wires of five different lengths $(1,2,3,4$ and $5\,m )$ but of same cross section $\left(2\,mm ^{2}\right)$ were taken and curves between extension and load were obtained. The slope (extension/load) of the curves were plotted with the wire length and the following graph is obtained. If the Young's modulus of given steel wires is $x \times 10^{11}\,Nm ^{-2}$, then the value of $x$ isView Solution
- 7A 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 ............... $N / m ^2$View Solution
- 8A wire suspended vertically from one of its ends is stretched by attaching a weight of $200\, N$ to the lower end. The weight stretches the wire by $1\, mm$ Then the elastic energy stored in the wire is ........ $J$View Solution
- 9A $5$ metre long wire is fixed to the ceiling. A weight of $10\, kg$ is hung at the lower end and is $1$ metre above the floor. The wire was elongated by $1\, mm$. The energy stored in the wire due to stretching is ......... $ joule$View Solution
- 10Three bars having length $l, 2l$ and $3l$ and area of cross-section $A, 2 A$ and $3 A$ are joined rigidly end to end. Compound rod is subjected to a stretching force $F$. The increase in length of rod is (Young's modulus of material is $Y$ and bars are massless)View Solution