The units of Young's modulus of elasticity are

$A$ 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 $]$

The ratio of Young's modulus of three wires is $2 : 2 : 1$ and the ratio of their cross-sectional areas is $1 : 2 : 3$. If the same force is applied to each,what is the ratio of the increase in their lengths?

The proportional limit of steel is $8 \times 10^8 \, N/m^2$ and its Young's modulus is $2 \times 10^{11} \, N/m^2$. The maximum elongation,a one metre long steel wire can be given without exceeding the elastic limit is ...... $mm$.

$A$ load of $1 \,kg$ weight is attached to one end of a steel wire of area of cross-section $3 \,mm^2$ and Young's modulus $10^{11} \,N/m^2$. The other end is suspended vertically from a hook on a wall, then the load is pulled horizontally and released. When the load passes through its lowest position, the fractional change in length is $(g = 10 \,m/s^2)$.

$A$ steel wire of length $L$ at $40^{\circ}C$ is suspended from the ceiling and then a mass $m$ is hung from its free end. The wire is cooled down from $40^{\circ}C$ to $30^{\circ}C$ to regain its original length $L$. The coefficient of linear thermal expansion of the steel is $10^{-5} /^{\circ}C$,Young's modulus of steel is $10^{11} N/m^2$,and the radius of the wire is $1 mm$. Assume that $L \gg$ diameter of the wire. Then the value of $m$ in $kg$ is nearly: