Two separate wires $A$ and $B$ are stretched by $2 \,mm$ and $4\, mm$ respectively, when they are subjected to a force of $2\, N$. Assume that both the wires are made up of same material and the radius of wire $B$ is 4 times that of the radius of wire $A$. The length of the wires $A$ and $B$ are in the ratio of $a : b$. Then $a / b$ can be expressed as $1 / x$ where $x$ is

A wire of length $L$ and radius $r$  is clamped rigidly at one end. When the other end of the wire is pulled by a force $f$ its length increases by $l$. Another wire of the same material of length $2L$ and radius $2r$  is pulled by a force $2f$. Then find the increase in length of this wire.

A truck is pulling a car out of a ditch by means of a steel cable that is $9.1\,m$ long and has a radius of $5\,mm$, when the car just begins to move the tension in the cable is $800\,N$. How much has the cable stretched ? (Young’s modulus for steel is $ 2 \times 10^{11}\,Nm^{-2}$)

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

A stress of $1.5\,kg.wt/mm^2$ is applied to a wire of Young's modulus $5 \times 10^{11}\,N/m^2$ . The percentage increase in its length is

The units of Young ‘s modulus of elasticity are