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?

$A$ load of $1 \,kg$ weight is attached to one end of a steel wire of area of cross-section $3 \,mm^2$ and Young's modulus $10^{11} \,N/m^2$. The other end is suspended vertically from a hook on a wall, then the load is pulled horizontally and released. When the load passes through its lowest position, the fractional change in length is $(g = 10 \,m/s^2)$.

$A$ uniform metallic wire is elongated by $0.04\, m$ when subjected to a linear force $F$. The elongation,if its length and diameter are doubled and subjected to the same force,will be ..... $cm$.

Young's modulus of the material of a wire of length $L$ and cross-sectional area $A$ is $Y$. If the length of the wire is doubled and the cross-sectional area is halved,then the Young's modulus will be:

If Young's modulus of iron is $2 \times 10^{11} \ N/m^2$ and the interatomic spacing between two molecules is $3 \times 10^{-10} \ m$,the interatomic force constant is ......... $N/m$.

Two rods of different materials having coefficients of linear expansion $\alpha_1, \alpha_2$ and Young's moduli $Y_1$ and $Y_2$ respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If $\alpha_1 : \alpha_2 = 2 : 3$,and the thermal stresses developed in the two rods are equal,then the ratio $Y_1 : Y_2$ is equal to: