The force required to stretch a steel wire of area of cross-section $1 \,mm^2$ to double its length is (Young's modulus of steel $= 2 \times 10^{11} \,N \,m^{-2}$)

If the temperature of a wire of length $2 \,m$ and area of cross-section $1 \,cm^2$ is increased from $0^{\circ}C$ to $80^{\circ}C$ and is not allowed to increase in length,then the force required for it is ............$N$ $\{Y=10^{10} \,N/m^2, \alpha=10^{-6}/^{\circ}C\}$

In steel,the Young's modulus and the strain at the breaking point are $2 \times 10^{11} \, N/m^2$ and $0.15$ respectively. The stress at the breaking point for steel is therefore:

$A$ steel wire of length $L$ and area of cross-section $A$ is suspended from a rigid support. If $Y$ is the Young's modulus of the material of the wire and $\alpha$ is the coefficient of linear expansion,then the increase in tension when the temperature falls by $t^{\circ} C$ is:

$A$ metal wire with circular cross-section and length $1 \,m$ is pulled with a tensile force of $1000 \,N$ on each side. For the wire to be stretched not more than $0.25 \,cm$, the minimum diameter of the wire required is (Young's modulus of the metal $= 10^{11} \,Pa$, take $\sqrt{\pi} = 1.77$). (in $\,mm$)

Two wires $A$ and $B$ are stretched by the same force. If,for $A$ and $B$,$Y_A: Y_B = 1: 2$,$r_A: r_B = 3: 1$,and $L_A: L_B = 4: 1$,then the ratio of their extension $\left(\frac{\Delta L_A}{\Delta L_B}\right)$ will be .............