If the length of a wire is doubled and its radius is halved, keeping the force constant, how does the elongation change?

A steel wire has length $2\,\,m$, radius $1{\rm{ }}mm$ and $Y = 2 imes {10^{11}}\,{\rm{N}}{{\rm{m}}^{ - 2}}$. A $1$ kg sphere is attached to one end of the wire and whirled in a vertical circle with an angular velocity of $2$ revolutions per second. When the sphere is at the lowest point of the vertical circle, the elongation of the wire is nearly (Take g = $10\,\,{\rm{m}}{{\rm{s}}^{ - 2}})$

Find the extension produced in a copper of length ${\rm{2}}\,\,{\rm{m}}$ and diameter ${\rm{3}}\,\,{\rm{mm}}$, when a force of ${\rm{30}}\,\,{\rm{N}}$ is applied. Young’s modulus for copper $= 1.1\,\, imes {10^{11}}\,\,{\rm{N}}{{\rm{m}}^{ - 2}}$

Consider an iron rod of length $1{\rm{ }}m$ and cross-section ${\rm{1}}\,\,{\rm{c}}{{\rm{m}}^2}$ with a Young’s modulus of ${10^{12}}$ dyne ${\rm{c}}{{\rm{m}}^{ - 2}}$. We wish to calculate the force with which the two ends must be pulled to produce an elongation of $1{\rm{ }}mm$. It is equal to

The length of a metal wire is $10\,cm$ when the tension in it is $20N$ and $12cm$. When the tension is $40N$. The natural length of the wire in $cm$ is

Which of the following properties is most crucial for determining the stretching of a spring?

Young’s modulus of the wire depends on

When a wire of length $10\,\,m$ is subjected to a force of $100\,\,N$ along its length, the lateral strain produced is $0.01 imes {10^{ - 3}}m$. The Poisson’s ratio was found to be $0.4$. If the area of cross-section of wire is $0.025\,\,{{\rm{m}}^2}$, its Young’s modulus is

To break a wire of one metre length, minimum $40\;kg\;wt$, is required. Then the wire of the same material of double radius and 6 m length will require breaking weight

Two wires of the same material have lengths in the ratio ${\rm{1 : 2}}$ and their radii are in the ratio $1{\rm{ }}:\sqrt 2$ If they are stretched by applying equal forces, the increase in their lengths will be in the ratio

A steel rod with $y = 2.0 imes {10^{11}}N{m^{ - 2}}$ and $\alpha = {10^5}{C^{ - 1}}$ of length and area of cross-section $10\,c{m^2}$ is heated from ${0^0}C$ to ${400^0}C$ without being allowed to extend. The tension produced in the rod is $X imes {10^5}N$, where the value of $x$ is