Four uniform wires of the same material are stretched by the same force. The dimensions of the wires are given below. Which one has the minimum elongation?

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 $.00$)

Column $-II$ is related to Column $-I$. Join them appropriately:

Column $-I$	Column $-II$
$(a)$ When temperature is raised,Young's modulus of a body	$(i)$ Zero
$(b)$ Young's modulus for air	$(ii)$ Infinite
	$(iii)$ Decreases
	$(iv)$ Increases

The proportional limit of steel is $8 \times 10^8 \, N/m^2$ and its Young's modulus is $2 \times 10^{11} \, N/m^2$. The maximum elongation,a one metre long steel wire can be given without exceeding the elastic limit is ...... $mm$.

$A$ brass wire of length $2 \ m$ and radius $1 \ mm$ at $27 ^\circ C$ is held taut between two rigid supports. Initially, it was cooled to a temperature of $-43 ^\circ C$, creating a tension $T$ in the wire. The temperature to which the wire has to be cooled in order to increase the tension in it to $1.4 \ T$ is . . . . . . $^\circ C$.

$A$ force is applied to a steel wire '$A$',rigidly clamped at one end. As a result,the elongation in the wire is $0.2\,mm$. If the same force is applied to another steel wire '$B$' of double the length and a diameter $2.4$ times that of the wire '$A$',the elongation in the wire '$B$' will be $............\times 10^{-2}\,mm$ (wires having uniform circular cross sections).