The mass and length of a wire are $M$ and $L$ respectively. The density of the material of the wire is $d$. On applying a force $F$ on the wire,the increase in length is $l$. Then,the Young's modulus of the material of the wire will be:

Young's modulus of a perfectly rigid body material is

The ratio of diameters of two wires of the same material is $n : 1$. The length of each wire is $4 \ m$. On applying the same load,the increase in length of the thin wire will be:

Young's modulus of rubber is $10^4 \ N/m^2$ and the area of cross-section is $2 \ cm^2$. If a force of $2 \times 10^5 \ dynes$ is applied along its length,then its initial length $L$ becomes:

As shown in the figure,in an experiment to determine Young's modulus of a wire,the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of $45^{\circ}$ with the load axis. The length of the wire is $62.8\,cm$ and its diameter is $4\,mm$. The Young's modulus is found to be $x \times 10^4\,N/m^2$. The value of $x$ is

$A$ steel rod of length $1\,m$ and area of cross-section $1\,cm^2$ is heated from $0\,^{\circ}C$ to $200\,^{\circ}C$ without being allowed to extend or bend. Find the tension produced in the rod $(Y = 2.0 \times 10^{11}\,N/m^2, \alpha = 10^{-5} \,^{\circ}C^{-1})$.