In an experiment, brass and steel wires of length $1\,m$ each with areas of cross section $1\,mm^2$ are used. The wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress requires to produced a new elongation of $0.2\,mm$ is [Given, the Young’s Modulus for steel and brass are respectively $120\times 10^9\,N/m^2$ and $60\times 10^9\,N/m^2$ ]

A wire of length $L,$ area of cross section $A$ is hanging from a fixed support. The length of the wire changes to $L_{1}$ when mass $M$ is suspended from its free end. The expression for Young's modulus is 

A metal wire of length $L_1$ and area of cross section $A$ is attached to a rigid support. Another metal wire of length $L_2$ and of the same cross sectional area is attached to the free end of the first wire. A body of mass $M$ is then suspended from the free end of the second wire. If $Y_1$ and $Y_2$ are the Youngs moduli of the wires respectively, the effective force constant of the system of two wires is :

A force of $200\, N$ is applied at one end of a wire of length $2\, m$ and having area of cross-section ${10^{ – 2}}\,c{m^2}$. The other end of the wire is rigidly fixed. If coefficient of linear expansion of the wire $\alpha = 8 \times 10{^{-6}}°C^{-1}$ and Young's modulus $Y = 2.2 \times {10^{11}}\,N/{m^2}$ and its temperature is increased by $5°C$, then the increase in the tension of the wire will be …….. $N$

A steel rod has a radius of $20\,mm$ and a length of $2.0\,m$. A force of $62.8\,kN$ stretches it along its length. Young's modulus of steel is $2.0 \times 10^{11}\,N / m ^2$. The longitudinal strain produced in the wire is $……….\times 10^{-5}$