Young's moduli of two wires $A$ and $B$ are in the ratio $7 : 4$. Wire $A$ is $2\, m$ long and has radius $R$. Wire $B$ is $1.5\, m$ long and has radius $2\, mm$. If the two wires stretch by the same length for a given load,then the value of $R$ is close to ......... $mm$.

Which material has a higher Young's modulus: copper or steel?

At $40\,^oC$,a brass wire of radius $0.5\, mm$ (diameter $1\, mm$) is hung from the ceiling. $A$ small mass $M$ is hung from the free end of the wire. When the wire is cooled down from $40\,^oC$ to $20\,^oC$,it regains its original length of $0.2\, m$. The value of $M$ is close to ........$kg$. (Coefficient of linear expansion $\alpha = 10^{-5}/^oC$ and Young's modulus $Y = 10^{11}\, N/m^2$; $g = 10\, ms^{-2}$)

$A$ force $F$ is applied on a wire of radius $r$ and length $L$,and the change in the length of the wire is $l$. If the same force $F$ is applied on a wire of the same material with radius $2r$ and length $2L$,then what is the change in the length of the second wire?

If the given graph shows the load $(W)$ attached to and the elongation $(\Delta l)$ produced in a wire of length $1 \,m$ and area of cross-section $1 \,mm^2$, then the Young's modulus of the material of the wire is

Two wires of diameter $0.25 \; cm,$ one made of steel and the other made of brass,are loaded as shown in the figure. The unloaded length of the steel wire is $1.5 \; m$ and that of the brass wire is $1.0 \; m.$ Compute the elongations of the steel and the brass wires. (Given: Young's modulus of steel $Y_s = 2.0 \times 10^{11} \; Pa,$ Young's modulus of brass $Y_b = 0.91 \times 10^{11} \; Pa$)