$A$ rod of uniform cross-sectional area $A$ and length $L$ has a weight $W$. It is suspended vertically from a fixed support. If Young's modulus for the rod is $Y$,then the elongation produced in the rod due to its own weight is:

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 $3M$.

In an experiment to determine the Young's modulus of a wire of length exactly $1\;m$,the extension in the length of the wire is measured as $0.4\;mm$ with an uncertainty of $\pm 0.02\;mm$ when a load of $1\;kg$ is applied. The diameter of the wire is measured as $0.4\;mm$ with an uncertainty of $\pm 0.01\;mm$. The error in the measurement of Young's modulus $(\Delta Y)$ is found to be $x \times 10^{10}\;N/m^2$. The value of $x$ is (Take $g = 10\;m/s^2$)

An iron rod of length $2\, m$ and cross-sectional area of $50\, mm^2$ is stretched by $0.5\, mm$ when a mass of $250\, kg$ is hung from its lower end. The Young's modulus of the iron rod is:

The ratio of the areas of cross-sections of three wires is $1:2:3$ and the ratio of the Young's moduli of their materials is $3:2:1$. If the three wires are of the same length and the same stretching force is applied to the three wires, then the ratio of the elongations of the three wires is

The force constant of a wire does not depend on