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)

A structural steel rod has a radius of $10 \;mm$ and a length of $1.0 \;m$. A $100 \;kN$ force stretches it along its length. Calculate $(a)$ stress, $(b)$ elongation, and $(c)$ strain on the rod. Young's modulus, of structural steel $1 s 2.0 \times 10^{11} \;N m ^{-2}$

A mild steel wire of length $1.0 \;m$ and cross-sectional area $0.50 \times 10^{-2} \;cm ^{2}$ is stretched, well within its elastic limit, horizontally between two pillars. A mass of $100 \;g$ is suspended from the mid-point of the wire. Calculate the depression at the midpoint.

A steel wire of diameter $2 \,mm$ has a breaking strength of $4 \times 10^5 \,N$.the breaking force ......... $\times 10^5 \,N$ of similar steel wire of diameter $1.5 \,mm$ ?

Two metallic wires $P$ and $Q$ have same volume and are made up of same material. If their area of cross sections are in the ratio $4: 1$ and force $F_1$ is applied to $\mathrm{P}$, an extension of $\Delta l$ is produced. The force which is required to produce same extension in $Q$ is $\mathrm{F}_2$.The value of $\frac{\mathrm{F}_1}{\mathrm{~F}_2}$ is__________.