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

$A$ steel wire is $1 \,m$ long and $1 \,mm^2$ in area of cross-section. If it takes $200 \,N$ to stretch this wire by $1 \,mm$,how much force will be required to stretch a wire of the same material as well as diameter from its normal length of $10 \,m$ to a length of $1002 \,cm$?

Stress required in a wire to produce $0.1\%$ strain is $4 \times 10^8 \, N/m^2$. Its Young's modulus is $Y_1$. If stress required in another wire to produce $0.3\%$ strain is $6 \times 10^8 \, N/m^2$,and its Young's modulus is $Y_2$,which relation is correct?

$A$ one metre steel wire of negligible mass and area of cross-section $0.01 \,cm^2$ is kept on a smooth horizontal table with one end fixed. $A$ ball of mass $1 \,kg$ is attached to the other end. The ball and the wire are rotating with an angular velocity of $\omega$. If the elongation of the wire is $2 \,mm$, then $\omega$ is (Young's modulus of steel $= 2 \times 10^{11} \,N/m^2$)

$A$ rigid bar of mass $15 \, kg$ is supported symmetrically by three wires,each $2 \, m$ long. The wires at each end are made of copper,and the middle one is made of steel. The Young's modulus of elasticity for copper and steel are $110 \times 10^9 \, N/m^2$ and $190 \times 10^9 \, N/m^2$ respectively. If each wire is to have the same tension,the ratio of their diameters (diameter of copper wire to diameter of steel wire) will be ............

What should be the diameter of a copper wire $(Y=12 \times 10^{10} \text{ N/m}^2)$ of length $5 \text{ m}$ to produce the same elongation produced by a $5 \text{ m}$ long aluminium wire $(Y=7 \times 10^{10} \text{ N/m}^2)$ of diameter $3 \text{ mm}$ with the same $40 \text{ kg}$ mass (in $\text{ mm}$)?