Which of the following materials generally has the highest Young's modulus?

A steel ring of radius $r$ and cross-sectional area 'A' is fitted onto a wooden disc of radius R(R > r). If Young’s modulus be $E$, then the force with which the steel ring is expanded is

Two wires are made of the same material and have the same volume. However, wire $1$ has cross-sectional area $A$ and wire $2$ has cross-sectional area $3\,A$. If the length of wire $1$ increases by $\Delta x$ on applying force $F$, how much force is needed to stretch wire $2$ by the same amount?

A rectangular bar $2\,\,cm$ in breadth and $1\,\,cm$ in depth and $100\,\,cm$ in length is supported at its ends and a load of $2$ kg is applied at its middle. If Young’s modulus of the material of the bar is $20\,\, imes \,\,{10^{11}}\,\,{\rm{dyne c}}{{\rm{m}}^{ - 2}},$, the depression in the bar is

A wire is stretched by $0.01\,m$ by a certain force $F$. Another wire of same material whose diameter and length are double to the original wire is stretched by the same force. Then its elongation will be

Two wires of the same material and length are stretched by the same force. Their masses are in the ratio ${\rm{3:2}}$. Their elongations are 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

Two springs made of the same material have the same volume. The first spring has cross-sectional area $A$ and the second spring has cross-sectional area $5A$. If a force $F$ stretches the first spring by $x$, what force is required to stretch the second spring by the same amount?

The length of a rubber cord is ${l_1}$ metre when the tension is ${\rm{4 N}}$ and ${l_2}$ metre when the tension is ${\rm{6 N}}$. The length when the tension is ${\rm{9 N}}$, is

If work done in stretching a wire by $1\,\,mm$ is $2{\rm{ }}J$, the work necessary for stretching another wire of same material, but wire double the radius and half length $1\,\,mm$ joule is

The diameter of a brass wire is ${\rm{0}}{\rm{.6 mm}}$ and $Y$ is $9 imes {10^6}\,\,{\rm{N}}{{\rm{m}}^{ - 2}}$ . The force which will increase its length by ${\rm{0}}{\rm{.2}}\,\,{\rm{\% }}$ is about