Two exactly similar wires of steel and copper are stretched by equal forces. If the difference in their elongations is $0.5$ cm, the elongation $(l)$ of each wire is ${Y_s}({\rm{steel}}) = 2.0 \times {10^{11}}\,N/{m^2}$${Y_c}({\rm{copper}}) = 1.2 \times {10^{11}}\,N/{m^2}$
Medium
Download our app for free and get started
(a) $l \propto \frac{1}{Y} \Rightarrow \frac{{{Y_s}}}{{{Y_c}}} = \frac{{{l_c}}}{{{l_s}}} \Rightarrow \frac{{{l_c}}}{{{l_s}}} = \frac{{2 \times {{10}^{11}}}}{{1.2 \times {{10}^{11}}}} = \frac{5}{3}$…(i)
Also ${l_c} - {l_s} = 0.5$…(ii)
On solving (i) and (ii) ${l_c} = 1.25\;cm$ and ${l_s} = 0.75\;cm$.
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
- 1A glass slab is subjected to a pressure of $10\, atm$. The fractional change in its volume is (Bulk modulus of glass $= 37 \times 10^9\, N\, m^{-2}$, $1\, atm = 1 \times 10^5\, N\, m^{-2}$)View Solution
- 2A copper wire $(Y = 1 \times 10^{11}\, N/m^2)$ of length $6\, m$ and a steel wire $(Y = 2 \times 10^{11}\, N/m^2)$ of length $4\, m$ each of cross section $10^{-5}\, m^2$ are fastened end to end and stretched by a tension of $100\, N$. The elongation produced in the copper wire is ......... $mm$View Solution
- 3A wire of cross-sectional area $3\,m{m^2}$ is first stretched between two fixed points at a temperature of $20°C$. Determine the tension when the temperature falls to $10°C$. Coefficient of linear expansion $\alpha = {10^{ - 5}} { ^\circ}{C^{ - 1}}$ and $Y = 2 \times {10^{11}}\,N/{m^2}$ ........ $N$View Solution
- 4$1\, m^3$ water is brought inside the lake upto $200$ metres depth from the surface of the lake. What will be change in the volume when the bulk modulus of elastically of water is $22000$ atmosphere? (density of water is $1\times10^3\, kg/m^3$ atmosphere pressure $= 10^5\, N/m^2$ and $g = 10\, m/s^2$)View Solution
- 5View SolutionWhich one of the following substances possesses the highest elasticity
- 6A wire is suspended by one end. At the other end a weight equivalent to $20\, N$ force is applied. If the increase in length is $1.0\, mm$, the increase in energy of the wire will be ....... $joule$View Solution
- 7Two wires $A$ and $B $ of same length and of the same material have the respective radii ${r_1}$ and ${r_2}$. Their one end is fixed with a rigid support, and at the other end equal twisting couple is applied. Then the ratio of the angle of twist at the end of $A$ and the angle of twist at the end of $B $ will beView Solution
- 8Given below are two statements: one is labelled as Assertion$(A)$ and the other is labelled as Reason $(R).$View Solution
$Assertion$ $(A)$ : In Vernier calliper if positive zero error exists, then while taking measurements, the reading taken will be more than the actual reading.
$Reason$ $(R)$ : The zero error in Vernier Calliper might have happened due to manufacturing defect or due to rough handling.
In the light of the above statements, choose the correct answer from the options given below :
- 9A copper wire of length $4.0m$ and area of cross-section $1.2\,c{m^2}$ is stretched with a force of $4.8 \times {10^3}$ $N.$ If Young’s modulus for copper is $1.2 \times {10^{11}}\,N/{m^2},$ the increase in the length of the wire will beView Solution
- 10One end of a uniform rod of mass $m_1$ and crosssectional area $A$ is hung from a ceiling. The other end of the bar is supporting mass $m_2$. The stress at the midpoint isView Solution
