The cross-sectional area of each wire is $10^{-4} \, m^2$. What is the displacement of point $B$?

One end of the steel rod is clamped to the roof and the other end is attached to a mass of $1000 \,kg$ as shown in the figure. The length of the rod is $50 \,cm$ and its cross-sectional area is $1000 \,mm^2$. The change in the length of the rod due to the weight of the mass is (Young's modulus of steel $= 2 \times 10^{11} \,Nm^{-2}$ and acceleration due to gravity $= 10 \,ms^{-2}$) (in $\,mm$)

The length of a light string is $1.4 \ m$ when the tension on it is $5 \ N$. If the tension increases to $7 \ N$,the length of the string is $1.56 \ m$. The original length of the string is . . . . . . $m$.

$A$ 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 . . . . . . .

To double the length of an iron wire having $0.5 \, cm^2$ area of cross-section,the required force will be $(Y = 10^{12} \, dyne/cm^2)$.

Two blocks of mass $2 \ kg$ and $4 \ kg$ are connected by a metal wire going over a smooth pulley as shown in the figure. The radius of the wire is $4.0 \times 10^{-5} \ m$ and Young's modulus of the metal is $2.0 \times 10^{11} \ N/m^2$. The longitudinal strain developed in the wire is $\frac{1}{\alpha \pi}$. The value of $\alpha$ is [Use $g = 10 \ m/s^2$].