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 ......... $mm$.

$A$ metal wire with circular cross-section and length $1 \,m$ is pulled with a tensile force of $1000 \,N$ on each side. For the wire to be stretched not more than $0.25 \,cm$, the minimum diameter of the wire required is (Young's modulus of the metal $= 10^{11} \,Pa$, take $\sqrt{\pi} = 1.77$). (in $\,mm$)

$A$ copper wire $(Y = 1 \times 10^{11} \, N/m^2)$ of length $6 \, m$ and a steel wire $(Y = 2 \times 10^{11} \, N/m^2)$ of length $4 \, m$,each of cross-sectional area $10^{-5} \, m^2$,are fastened end to end and stretched by a tension of $100 \, N$. The elongation produced in the copper wire is ......... $mm$.

$A$ wire of length $L$ and radius $r$ is clamped rigidly at one end. When the other end of the wire is pulled by a force $f$,its length increases by $l$. Another wire of the same material of length $2L$ and radius $2r$ is pulled by a force $2f$. Then the increase in its length will be

An Indian rubber cord $L$ metre long and area of cross-section $A$ $m^2$ is suspended vertically. The density of rubber is $D$ $kg/m^3$ and Young's modulus of rubber is $E$ $N/m^2$. If the wire extends by $l$ metre under its own weight,then the extension $l$ is:

An area of cross-section of a rubber string is $2 \, cm^2$. Its length is doubled when stretched with a linear force of $2 \times 10^5 \, dynes$. The Young's modulus of the rubber in $dyne/cm^2$ will be: