Force constant of a spring $(K)$ is synonymous to

Two wires $A$ and $B$ of 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 .......

If the length of a wire is made double and radius is halved of its respective values. Then, the Young's modules of the material of the wire will :

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 $5\,cm$. Another wire of the same material of length $4 L$ and radius $4\,r$ is pulled by a force $4\,F$ under same conditions. The increase in length of this wire is $....cm$.

If in case $A$, elongation in wire of length $L$ is $l$, then for same wire elongation in case $B$ will be ......

Give the relation between shear modulus and Young’s modulus.