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 $= 2 \times 10^{11} \,N \,m^{-2}$)

The following four wires of length $L$ and radius $r$ are made of the same material. Which of these will have the largest extension,when the same tension is applied?

One end of a steel wire of radius $r$ is fixed to a ceiling and a load of $3 \ kg$ is attached to the free end of the wire. Another wire made of copper of radius $2r$ is attached to the bottom of the $3 \ kg$ load and a $2 \ kg$ load is attached to the free end of the copper wire. The ratio of longitudinal strains produced in copper and steel wires is (Young modulus of steel $= 20 \times 10^{10} \ Nm^{-2}$,Young modulus of copper $= 12 \times 10^{10} \ Nm^{-2}$)

Two wires $A$ and $B$ of the same length are made of the same material. The load $(F)$ vs. elongation $(x)$ graph for these two wires is shown in the figure. Which of the following statement$(s)$ is/are true?

Wires $A$ and $B$ are connected with blocks $P$ and $Q$ as shown. The ratio of lengths,radii,and Young's modulus of wires $A$ and $B$ are $r, 2r$,and $3r$ respectively ($r$ is a constant). Find the mass of block $P$ if the ratio of the increase in their corresponding lengths is $1/(6r^2)$. The mass of block $Q$ is $3M$.

Two wires made of the same material are clamped rigidly at one end and pulled by the same force on the other end. The length and the radius of the first wire are three times those of the second wire. If $x$ is the increase in the length of the first wire,then the increase in the length of the second wire is