To break a wire of $1 \, m$ length, a minimum weight of $40 \, kg \, wt$ is required. Then, the wire of the same material with double the radius and $6 \, m$ length will require a breaking weight of ....... $kg \, wt$.

Two steel wires of same length $L$ but radii $r$ and $2r$ are connected together end to end and tied to a wall as shown. The force $F$ stretches the combination by $10 \ mm$. How far does the junction point $A$ move (in $mm$)?

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 $g = 10\;m/s^2$)

$A$ uniform dense rod with non-uniform Young's modulus is hanging from the ceiling under gravity. If the elastic energy density at every point is the same,then how will Young's modulus change with $x$ as shown in the graphs?

Which of the following graphs correctly depicts the spring constant $k$ versus the length $l$ of the spring?

$A$ $4 \ kg$ 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: