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 $l$. Another wire of same material of length $2 L$ and radius $2 r$ is pulled by a force $2 f$. Then the increase in its length will be

A structural steel rod has a radius of $10\,mm$ and length of $1.0\,m.$ A $100\,kN$ force stretches it along its length . Young's modulus of structural steel is $2 \times 10^{11}\,Nm^{-2}.$ The percentage strain is about .......  $\%$

Read the following two statements below carefully and state, with reasons, if it is true or false.

$(a)$ The Young’s modulus of rubber is greater than that of steel;

$(b)$ The stretching of a coil is determined by its shear modulus.

A mild steel wire of length $2l$ meter cross-sectional area $A \;m ^2$ is fixed horizontally between two pillars. A small mass $m \;kg$ is suspended from the mid point of the wire. If extension in wire are within elastic limit. Then depression at the mid point of wire will be .............

The load versus elongation graph for four wires of same length and the same material is shown in figure. The thinnest wire is represented by line

If the ratio of lengths, radii and Young's moduli of steel and brass wires in the figure are $a, b$ and $c$ respectively, then the corresponding ratio of increase in their lengths is