If the given graph shows the load $(W)$ attached to and the elongation $(\Delta l)$ produced in a wire of length $1 \,m$ and area of cross-section $1 \,mm^2$, then the Young's modulus of the material of the wire is

The pressure that has to be applied to the ends of a steel wire of length $10 \ cm$ to keep its length constant when its temperature is raised by $100 \ ^\circ C$ is: (For steel,Young's modulus $Y = 2 \times 10^{11} \ N/m^2$ and coefficient of thermal expansion $\alpha = 1.1 \times 10^{-5} \ K^{-1}$)

Longitudinal stress of $1\,kg/mm^2$ is applied on a wire. The percentage increase in length is $(Y = 10^{11}\,N/m^2)$. (in $\%$)

$A$ steel rod has a radius of $20\,mm$ and a length of $2.0\,m$. $A$ force of $62.8\,kN$ stretches it along its length. Young's modulus of steel is $2.0 \times 10^{11}\,N/m^2$. The longitudinal strain produced in the wire is $..........\times 10^{-5}$.

In nature,the failure of structural members usually results from large torque because of twisting or bending rather than due to tensile or compressive strains. This process of structural breakdown is called buckling. In cases of tall cylindrical structures like trees,the torque is caused by their own weight bending the structure,such that the vertical line through the centre of gravity does not fall within the base. The elastic torque caused by this bending about the central axis of the tree is given by $\frac{Y\pi r^4}{4R}$,where $Y$ is the Young's modulus,$r$ is the radius of the trunk,and $R$ is the radius of curvature of the bent surface along the height of the tree containing the centre of gravity (the neutral surface). Estimate the critical height of a tree for a given radius of the trunk.

$A$ cylindrical rod made of aluminum has a length of $1 \,m$ and a diameter of $10 \,cm$. The rod is subjected to a tensile force of $100 \,kN$. Calculate the elongation in the rod. (Young's modulus of aluminum $= 70 \,GPa$)