The temperature of a wire of length $1$ metre and area of cross-section $1\,c{m^2}$ is increased from $0°C$ to $100°C$. If the rod is not allowed to increase in length, the force required will be $(\alpha = {10^{ - 5}}/^\circ C$ and $Y = {10^{11}}\,N/{m^2})$
Medium
Download our app for free and get started
(b) $F = $force developed$ = YA\alpha (\Delta \theta )$
$ = {10^{11}} \times {10^{ - 4}} \times {10^{ - 5}} \times 100 = {10^4}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 SolutionThe adiabatic elasticity of a gas is equal to
- 2If a load of $9$ $kg$ is suspended on a wire, the increase in length is $4.5\, mm$. The force constant of the wire isView Solution
- 3An Indian rubber cord $L$ metre long and area of cross-section $A$ $metr{e^2}$ is suspended vertically. Density of rubber is $D$ $kg/metr{e^3}$ and Young's modulus of rubber is $E$ $newton/metr{e^2}$. If the wire extends by $l$ metre under its own weight, then extension $l$ isView Solution
- 4A 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 $\times 10^{-10} {m}$)View Solution
- 5View SolutionWith rise in temperature, the Young's modulus of elasticity
- 6Steel and copper wires of same length are stretched by the same weight one after the other. Young's modulus of steel and copper are $2 \times {10^{11}}\,N/{m^2}$ and $1.2 \times {10^{11}}\,N/{m^2}$. The ratio of increase in lengthView Solution
- 7The bulk modulus of a spherical object is '$B$'. If it is subjected to uniform pressure '$P$', the fractional decrease in radius isView Solution
- 8When 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
- 9A steel wire of length ' $L$ ' at $40^{\circ}\,C$ is suspended from the ceiling and then a mass ' $m$ ' is hung from its free end. The wire is cooled down from $40^{\circ}\,C$ to $30^{\circ}\,C$ to regain its original length ' $L$ '. The coefficient of linear thermal expansion of the steel is $10^{-5} { }^{\circ}\,C$, Young's modulus of steel is $10^{11}\, N /$ $m ^2$ and radius of the wire is $1\, mm$. Assume that $L \gg $ diameter of the wire. Then the value of ' $m$ ' in $kg$ is nearlyView Solution
- 10A wire fixed at the upper end stretches by length $l$ by applying a force $F$. The work done in stretching isView Solution