What force is required to increase the length of a wire of diameter $4 \, mm$ and Young's modulus $9 \times 10^{10} \, N/m^2$ by $0.1\%$?

The length of an iron wire is $L$ and the area of cross-section is $A$. The increase in length is $l$ upon applying a force $F$ on its two ends. Which of the following statements is correct?

$A$ wire of cross-sectional area $10^{-6} \, m^2$ is stretched such that its length increases by $0.1\%$. If the tension produced in the wire is $1000 \, N$, calculate the Young's modulus of the wire.

$A$ wooden wheel of radius $R$ is made of two semicircular parts (see figure). The two parts are held together by a ring made of a metal strip of cross-sectional area $S$ and length $L$. $L$ is slightly less than $2\pi R$. To fit the ring on the wheel,it is heated so that its temperature rises by $\Delta T$ and it just slips over the wheel. As it cools down to the surrounding temperature,it presses the semicircular parts together. If the coefficient of linear expansion of the metal is $\alpha$,and its Young's modulus is $Y$,the force that one part of the wheel applies on the other part is:

$A$ thin rod having a length of $1\;m$ and area of cross-section $3 \times 10^{-6}\;m^2$ is suspended vertically from one end. The rod is cooled from $210^{\circ}C$ to $160^{\circ}C$. After cooling,a mass $M$ is attached at the lower end of the rod such that the length of the rod again becomes $1\;m$. Young's modulus and coefficient of linear expansion of the rod are $2 \times 10^{11}\;Nm^{-2}$ and $2 \times 10^{-5}\;K^{-1}$,respectively. The value of $M$ is $.......kg$. (Take $g=10\;ms^{-2}$)

An area of cross-section of a rubber string is $2 \, cm^2$. Its length is doubled when stretched with a linear force of $2 \times 10^5 \, dynes$. The Young's modulus of the rubber in $dyne/cm^2$ will be: