A wire is stretched $1{\rm{ }}mm$ by a force of $1{\rm{ }}k{\rm{ }}N$. How far would a wire of the same material and length but of four times that diameter be stretched by the same force ?

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

A wire of length L and cross-sectional area A is stretched by a force F. If Young's modulus of the material of the wire is Y, the elongation produced in the wire is:

A wire of length ${\rm{L}}$, area of cross section ${\rm{A}}$ is hanging from a fixed support. The length of the wire changes to ${{\rm{L}}_{\rm{1}}}$ when mass ${\rm{M}}$ is suspended from its free end. The expression for Young’s modulus is:

A metal bar of length $1 \mathrm{m}$ is fixed between two rigid supports. The bar's Young's modulus is $1.5 imes 10^{11} \mathrm{N} \mathrm{m}^{-2}$, and its coefficient of linear thermal expansion is 1 imes 10^{-5} \, ^{\circ}C^{-1}. If the temperature is lowered by $20^{\circ} \mathrm{C}$, what tensile stress will be developed in the bar?

If the compressibility of water is $\sigma$ per unit atmospheric pressure, then the decrease in volume ($V$)  due to p, atmospheric pressure will be :

Two cylinders of the same material and equal volume have cross-sectional areas $A$ and $4A$. If a force $F$ stretches the first cylinder by $\Delta l$, what force is needed to stretch the second cylinder by $2\Delta l$?

When a weight of $5\,\,kg$ is suspended from a copper wire of length $30\,\,m$ and diameter $0.5\,\,mm$, the length of the wire increases by $2.4\,\,cm$. If the diameter is doubled, the extension produced is

One end of steel wire is fixed to ceiling of an elevator moving up with an acceleration ${\rm{2}}\,\,{\rm{m}}{{\rm{s}}^{ - 2}}$ and a load of ${\rm{10}}$ kg hangs from other end. Area of cross-section of the wire is $2\,\,{\rm{c}}{{\rm{m}}^2}$. The longitudinal strain in the wire is (Take g$= 10\,\,{\rm{m}}{{\rm{s}}^{ - 2}}\,\,{\rm{and}}\,{\rm{ Y}} = 2\,\, imes {10^{11}}\,{\rm{N}}{{\rm{m}}^{ - 2}})$

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