What force is required to stretch a wire of cross-sectional area $1 \, cm^2$ to $1.1$ times its original length? (Given: Young's modulus $Y = 2 \times 10^{11} \, N/m^2$)

The stress versus strain graphs for wires of two materials $A$ and $B$ are as shown in the figure. If $Y_A$ and $Y_B$ are the Young's modulus of the materials,then

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?

$A$ rod of length $L$ and radius $r$ is held between two rigid walls so that it is not allowed to expand. If its temperature is increased,then the force developed in it is proportional to .........

The elongation of a wire on the surface of the earth is $10^{-4} \; m$. The same wire of same dimensions is elongated by $6 \times 10^{-5} \; m$ on another planet. The acceleration due to gravity on the planet will be $\dots \; m/s^2$. (Take acceleration due to gravity on the surface of earth $= 10 \; m/s^2$)

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: