$A$ $0.1 \,kg$ mass is suspended from a wire of negligible mass. The length of the wire is $1 \,m$ and its cross-sectional area is $4.9 \times 10^{-7} \,m^2$. If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency $140 \,rad \,s^{-1}$. If the Young's modulus of the material of the wire is $n \times 10^9 \,N \,m^{-2}$, the value of $n$ is

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,$Y_{\text{steel}} = 20 \times 10^{11} \,dyne/cm^2$,$Y_{\text{copper}} = 12 \times 10^{11} \,dyne/cm^2$.

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

What is the percentage increase in length of a wire of diameter $2.5 \,mm$,stretched by a force of $100 \,kg$ wt? (Young's modulus of elasticity of wire $= 12.5 \times 10^{11} \,dyne/cm^2$)

The length of a metal wire is $L$, when it is subjected to tension $T$. If the tension is increased to $T+\Delta T$, the length becomes $L+\Delta L$. The natural length of the wire is

The speed of a transverse wave passing through a string of length $50 \; cm$ and mass $10 \; g$ is $60 \; ms^{-1}$. The area of cross-section of the wire is $2.0 \; mm^2$ and its Young's modulus is $1.2 \times 10^{11} \; Nm^{-2}$. The extension of the wire over its natural length due to its tension will be $x \times 10^{-5} \; m$. The value of $x$ is $...$