Two wires made of the same material are clamped rigidly at one end and pulled by the same force on the other end. The length and the radius of the first wire are three times those of the second wire. If $x$ is the increase in the length of the first wire,then the increase in the length of the second wire is

If the ratio of diameters,lengths and Young's moduli of steel and brass wires shown in the figure are $p, q$ and $r$ respectively,then the corresponding ratio of increase in their lengths would be

$A$ thin rod having a length of $1\;m$ and area of cross-section $3 \times 10^{-6}\;m^2$ is suspended vertically from one end. The rod is cooled from $210^{\circ}C$ to $160^{\circ}C$. After cooling,a mass $M$ is attached at the lower end of the rod such that the length of the rod again becomes $1\;m$. Young's modulus and coefficient of linear expansion of the rod are $2 \times 10^{11}\;Nm^{-2}$ and $2 \times 10^{-5}\;K^{-1}$,respectively. The value of $M$ is $.......kg$. (Take $g=10\;ms^{-2}$)

At $40\,^oC$,a brass wire of radius $0.5\, mm$ (diameter $1\, mm$) is hung from the ceiling. $A$ small mass $M$ is hung from the free end of the wire. When the wire is cooled down from $40\,^oC$ to $20\,^oC$,it regains its original length of $0.2\, m$. The value of $M$ is close to ........$kg$. (Coefficient of linear expansion $\alpha = 10^{-5}/^oC$ and Young's modulus $Y = 10^{11}\, N/m^2$; $g = 10\, ms^{-2}$)

$A$ wire of length $L$ is hanging from a fixed support. The length changes to $L_{1}$ and $L_{2}$ when masses $1 \, kg$ and $2 \, kg$ are suspended respectively from its free end. Then the value of $L$ is equal to:

$A$ load of $1 \,kg$ weight is attached to one end of a steel wire of area of cross-section $3 \,mm^2$ and Young's modulus $10^{11} \,N/m^2$. The other end is suspended vertically from a hook on a wall, then the load is pulled horizontally and released. When the load passes through its lowest position, the fractional change in length is $(g = 10 \,m/s^2)$.