Two wires of same length having radius of $2 \ mm$ and $1.5 \ mm$ respectively are loaded with same weights. Extension of the second wire is double than that of the first wire. What is the ratio of the Young's modulus of the first wire to that of the second wire?

$A$ wire is suspended from a rigid support and a weight $W$ is attached to its free end,causing an extension of $1.0 \, mm$. If the same wire is passed over a pulley and a weight $W$ is attached to each of its two ends,what will be the extension in the wire in $mm$?

$A$ one metre steel wire of negligible mass and area of cross-section $0.01 \,cm^2$ is kept on a smooth horizontal table with one end fixed. $A$ ball of mass $1 \,kg$ is attached to the other end. The ball and the wire are rotating with an angular velocity of $\omega$. If the elongation of the wire is $2 \,mm$, then $\omega$ is (Young's modulus of steel $= 2 \times 10^{11} \,N/m^2$)

The two wires $A$ and $B$ of equal cross-section but of different materials are joined together. The ratio of Young's modulus of wire $A$ and wire $B$ is $20/11$. When the joined wire is kept under certain tension the elongations in the wires $A$ and $B$ are equal. If the length of wire $A$ is $2.2\text{ m}$, then the length of wire $B$ is . . . . . . m.

$A$ steel wire $1.5\,m$ long and of radius $1\,mm$ is attached with a load of $3\,kg$ at one end,while the other end is fixed. It is whirled in a vertical circle with a frequency of $2\,Hz$. Find the elongation of the wire when the weight is at the lowest position. (Given: $Y = 2 \times 10^{11}\,N/m^2$ and $g = 10\,m/s^2$)

The Young's modulus of a wire of length $L$ and radius $r$ is $Y$. If the length is reduced to $\frac{L}{2}$ and radius is $\frac{r}{2}$,then the Young's modulus will be