$A$ wire of length $L$ and radius $r$ is rigidly fixed at one end. On stretching the other end of the wire with a force $F$,the increase in length is $l$. If another wire of the same material but double the length and double the radius is stretched with a force $2F$,then the increase in length is:

$A$ steel ring of radius $r$ and cross-sectional area $A$ is fitted onto a wooden disc of radius $R$ $(R > r)$. If Young's modulus is $Y$,then the force with which the steel ring is expanded is

Two wires are made of the same material and have the same volume. The first wire has cross-sectional area $A$ and the second wire has cross-sectional area $3A$. If the length of the first wire is increased by $\Delta l$ on applying a force $F$,how much force is needed to stretch the second wire by the same amount?

$A$ 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 $2 \times 10^{11}\,N/m^2.$ The percentage strain is about ....... $\%$

An object of mass $m$ is suspended at the end of a massless wire of length $L$ and area of cross-section $A$. The Young's modulus of the material of the wire is $Y$. If the mass is pulled down slightly,its frequency of oscillation along the vertical direction is:

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