One end of a horizontal thick copper wire of length $2L$ and radius $2R$ is welded to an end of another horizontal thin copper wire of length $L$ and radius $R$. When the arrangement is stretched by applying forces at two ends,the ratio of the elongation in the thin wire to that in the thick wire is:

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,while the other end is subjected to an elongation. The stress required to produce a total elongation of $0.2\,mm$ is: [Given: Young's Modulus for steel and brass are $120 \times 10^9\,N/m^2$ and $60 \times 10^9\,N/m^2$ respectively]

$A$ $100\,m$ long wire having cross-sectional area $6.25 \times 10^{-4}\,m^2$ and Young's modulus $10^{10}\,N/m^2$ is subjected to a load of $250\,N$. The elongation in the wire will be:

$A$ 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 $(g = 10 \,m/s^2)$.

$A$ steel wire and a copper wire are joined end to end having equal cross-sections. The elongation of the two wires is found to be equal under tension. What is the ratio of the length of the steel wire to the length of the copper wire? (Young's modulus of steel $= 2.0 \times 10^{11} \ N \ m^{-2}$ and Young's modulus of copper $= 1.1 \times 10^{11} \ N \ m^{-2}$)

In Young's experiment,if the length of the wire and the radius are both doubled,then the value of $Y$ will become: