The length of an elastic string is $x \, m$ when the tension is $8 \, N$ and $y \, m$ when the tension is $10 \, N$. The length in meters when the tension is $18 \, N$ is:

When a uniform wire of radius $r$ is stretched by a $2 \, kg$ weight,the increase in its length is $2.00 \, mm$. If the radius of the wire is $r/2$ and other conditions remain the same,the increase in its length is .......... $mm$. (in $.00$)

$A$ steel wire is $1 \,m$ long and $1 \,mm^2$ in area of cross-section. If it takes $200 \,N$ to stretch this wire by $1 \,mm$,how much force will be required to stretch a wire of the same material as well as diameter from its normal length of $10 \,m$ to a length of $1002 \,cm$?

$A$ wire of length $2\, m$ is made from $10\, cm^3$ of copper. $A$ force $F$ is applied so that its length increases by $2\, mm$. Another wire of length $8\, m$ is made from the same volume of copper. If the same force $F$ is applied to it,its length will increase by ......... $cm$.

An area of cross-section of a rubber string is $2 \, cm^2$. Its length is doubled when stretched with a linear force of $2 \times 10^5 \, dynes$. The Young's modulus of the rubber in $dyne/cm^2$ will be:

Two wires $A$ and $B$ of the same material have radii in the ratio $2:1$ and lengths in the ratio $4:1$. The ratio of the normal forces required to produce the same change in the lengths of these two wires is .......