The Young's modulus of a steel wire of length $6\,m$ and cross-sectional area $3\,mm ^2$, is $2 \times 11^{11}\,N / m ^2$. The wire is suspended from its support on a given planet. A block of mass $4\,kg$ is attached to the free end of the wire. The acceleration due to gravity on the planet is $\frac{1}{4}$ of its value on the earth. The elongation of wire is  (Take $g$ on the earth $=10$ $\left.m / s ^2\right):$

Each of three blocks $P$, $Q$ and $R$ shown in figure has a mass of $3 \mathrm{~kg}$. Each of the wire $A$ and $B$ has cross-sectional area $0.005 \mathrm{~cm}^2$ and Young's modulus $2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$. Neglecting friction, the longitudinal strain on wire $B$ is____________ $\times 10^{-4}$. $\left(\right.$ Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )

The pressure that has to be applied to the ends of a steel wire of length $10\ cm$ to keep its length constant when its temperature is raised by $100^o C$ is: (For steel Young's modulus is $2 \times 10^{11}$ $Nm^{-1}$ and coefficient of thermal expansion is $1.1 \times 10^{-5}$ $K^{-1}$ )

One end of a metal wire is fixed to a ceiling and a load of $2 \mathrm{~kg}$ hangs from the other end. A similar wire is attached to the bottom of the load and another load of $1 \mathrm{~kg}$ hangs from this lower wire. Then the ratio of longitudinal strain of upper wire to that of the lower wire will be____________.

[Area of cross section of wire $=0.005 \mathrm{~cm}^2$, $\mathrm{Y}=2 \times 10^{11}\  \mathrm{Nm}^{-2}$ and $\left.\mathrm{g}=10 \mathrm{~ms}^{-2}\right]$

A weight of $200 \,kg$ is suspended by vertical wire of length $600.5\, cm$. The area of cross-section of wire is $1\,m{m^2}$. When the load is removed, the wire contracts by $0.5 \,cm$. The Young's modulus of the material of wire will be

The length of wire, when $M_1$ is hung from it, is $I_1$ and is $I_2$ with both $M_1$ and $M_2$ hanging. The natural length of wire is ........