$A$ wire of area of cross-section $10^{-6} \ m^2$ is increased in length by $0.1 \%$. The tension produced is $1000 \ N$. The Young's modulus of the wire is:

On increasing the length by $0.5\, mm$ in a steel wire of length $2\, m$ and area of cross-section $2\, mm^2$,the force required is ($Y$ for steel $= 2.2 \times 10^{11}\, N/m^2$).

$A$ metal rod of length $L$ and cross-sectional area $A$ is heated through $T^{\circ} C$. What is the force required to prevent the expansion of the rod lengthwise? $[Y=$ Young's modulus of the material of rod,$\alpha=$ coefficient of linear expansion $]$

$A$ mild steel wire of length $2l$ meter and cross-sectional area $A \; m^2$ is fixed horizontally between two pillars. $A$ small mass $m \; kg$ is suspended from the midpoint of the wire. If the extension in the wire is within the elastic limit,then the depression $x$ at the midpoint of the wire will be:

The length of a light string is $1.4 \ m$ when the tension on it is $5 \ N$. If the tension increases to $7 \ N$,the length of the string is $1.56 \ m$. The original length of the string is . . . . . . $m$.

$A$ 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 is $Y$,then the force with which the steel ring is expanded is