The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?

$A$ metal string $A$ is suspended from a rigid support and its free end is attached to a block of mass $M$. $A$ second block having mass $2M$ is suspended at the bottom of the first block using a string $B$. The area of cross-sections of strings $A$ and $B$ are the same. The ratio of lengths of strings $A$ to $B$ is $2$ and the ratio of their Young's moduli $(Y_A/Y_B)$ is $0.5$. The ratio of elongations in $A$ to $B$ is . . . . . . .

Two wires each of radius $0.2\,cm$ and negligible mass, one made of steel and the other made of brass, are loaded as shown in the figure. The elongation of the steel wire is $.........\times 10^{-6}\,m$. [Young's modulus for steel $= 2 \times 10^{11}\,N/m^2$ and $g = 10\,m/s^2$]

$A$ $4 \ kg$ stone attached at the end of a steel wire is being whirled at a constant speed $12 \ ms^{-1}$ in a horizontal circle. The wire is $4 \ m$ long with a diameter $2.0 \ mm$ and Young's modulus of the steel is $2 \times 10^{11} \ Nm^{-2}$. The strain in the wire is:

What is the effect of change in temperature on the Young's modulus?

The dimensional formula for Young's modulus is