Two similar wires under the same load yield elongation of $0.1$ $mm$ and $0.05$ $mm$ respectively. If the area of cross- section of the first wire is $4m{m^2},$ then the area of cross section of the second wire is..... $mm^2$

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__________.

When a weight of $10\, kg$ is suspended from a copper wire of length $3$ metres and diameter $0.4\, mm,$ its length increases by $2.4\, cm$. If the diameter of the wire is doubled, then the extension in its length will be ........ $cm$

A cylindrical wire of radius $1\,\, mm$, length $1 m$, Young’s modulus $= 2 × 10^{11} N/m^2$, poisson’s ratio $\mu = \pi /10$ is stretched by a force of $100 N$. Its radius will become

Explain experimental determination of Young’s modulus.

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)