The value of Young's modulus for a perfectly rigid body is ...........

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.

$A$ uniform cylindrical rod of length $L$ and radius $r$ is made from a material whose Young's modulus of elasticity equals $Y$. When this rod is heated by temperature $T$ and simultaneously subjected to a net longitudinal compressional force $F$,its length remains unchanged. The coefficient of volume expansion of the material of the rod is (nearly) equal to:

In a human pyramid in a circus,the entire weight of the balanced group is supported by the legs of a performer who is lying on his back. The combined mass of all the persons performing the act,and the tables,plaques,etc.,involved is $280 \; kg$. The mass of the performer lying on his back at the bottom of the pyramid is $60 \; kg$. Each thighbone (femur) of this performer has a length of $50 \; cm$ and an effective radius of $2.0 \; cm$. Determine the amount by which each thighbone gets compressed under the extra load. (Take Young's modulus for bone $Y = 9.4 \times 10^9 \; N/m^2$)

The following four wires of length $L$ and radius $r$ are made of the same material. Which of these will have the largest extension,when the same tension is applied?

$A$ 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 $= 70 \,GPa$)