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

Which of the following graphs correctly depicts the spring constant $k$ versus the length $l$ of the spring?

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 .......

$A$ metallic ring of radius $r$ and cross-sectional area $A$ is fitted into a wooden circular disc of radius $R$ $(R > r)$. If the Young's modulus of the material of the ring is $Y$, the force with which the metal ring expands is

$A$ student performs an experiment to determine the Young's modulus of a wire of length $2 \, m$ using Searle's method. In an observation,for a load of $10 \, kg$,the extension of the wire is measured as $0.88 \, mm$ with an uncertainty of $\pm 0.05 \, mm$. The student also measures the diameter of the wire as $0.4 \, mm$ with an uncertainty of $\pm 0.01 \, mm$. Take $g = 9.8 \, m/s^2$ (exact). Calculate the Young's modulus of the wire.

$A$ copper wire and a steel wire of the same diameter and length are connected end to end and a force is applied,which stretches their combined length by $1 \ cm$. The two wires will have