A string of area of cross-section $4\,mm ^{2}$ and length $0.5$ is connected with a rigid body of mass $2\,kg$. The body is rotated in a vertical circular path of radius $0.5\,m$. The body acquires a speed of $5\,m / s$ at the bottom of the circular path. Strain produced in the string when the body is at the bottom of the circle is $\ldots . . \times 10^{-5}$. (Use Young's modulus $10^{11}\,N / m ^{2}$ and $g =10\,m / s ^{2}$ )

A steel wire $1.5\,m$ long and of radius $1\,mm$ is attached with a load $3\,kg$ at one end the other end of the wire is fixed it is whirled in a vertical circle with a frequency $2\,Hz$ . Find the elongation of the wire when the weight is at the lowest position $(Y = 2 \times 10^{11}\,N/m^2$ and $g = 10\,m/s^2)$

A bar is subjected to axial forces as shown. If $E$ is the modulus of elasticity of the bar and $A$ is its crosssection area. Its elongation will be

A uniform heavy rod of weight $10\, {kg} {ms}^{-2}$, crosssectional area $100\, {cm}^{2}$ and length $20\, {cm}$ is hanging from a fixed support. Young modulus of the material of the rod is $2 \times 10^{11} \,{Nm}^{-2}$. Neglecting the lateral contraction, find the elongation of rod due to its own weight. (In $\times 10^{-10} {m}$)

A force is applied to a steel wire ' $A$ ', rigidly clamped at one end. As a result elongation in the wire is $0.2\,mm$. If same force is applied to another steel wire ' $B$ ' of double the length and a diameter $2.4$ times that of the wire ' $A$ ', the elongation in the wire ' $B$ ' will be $…………\times 10^{-2}\,mm$ (wires having uniform circular cross sections)