$A$ block of mass $2 \ kg$ is tied to one end of a $2 \ m$ long metal wire of $1.0 \ mm^2$ area of cross-section and rotated in a vertical circle such that the tension in the wire is zero at the highest point. If the maximum elongation in the wire is $2 \ mm$, the Young's modulus of the metal is (Acceleration due to gravity $= 10 \ ms^{-2}$)

Two exactly similar wires of steel and copper are stretched by equal forces. If the total elongation is $2 \,cm$,then how much is the elongation in steel and copper wire respectively? Given,$Y_{\text{steel}} = 20 \times 10^{11} \,dyne/cm^2$,$Y_{\text{copper}} = 12 \times 10^{11} \,dyne/cm^2$.

The stress versus strain graphs for wires of two materials $A$ and $B$ are as shown in the figure. If $Y_A$ and $Y_B$ are the Young's modulus of the materials,then

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 $= 2.2 \times 10^{11}\, N/m^2$).

$A$ meter scale of mass $m$,Young's modulus $Y$,and cross-sectional area $A$ is hung vertically from the ceiling at the zero mark. The separation between the $30\ cm$ and $70\ cm$ marks will be: (Assume $\frac{mg}{AY}$ is dimensionless)

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 $Y = 9.4 \times 10^9 \; N/m^2$)