Two similar wires under the same load yield elongations of $0.1 \ mm$ and $0.05 \ mm$ respectively. If the area of cross-section of the first wire is $4 \ mm^2$,then the area of cross-section of the second wire is..... $mm^2$.

One end of a horizontal thick copper wire of length $2L$ and radius $2R$ is welded to an end of another horizontal thin copper wire of length $L$ and radius $R$. When the arrangement is stretched by applying forces at two ends,the ratio of the elongation in the thin wire to that in the thick wire is:

Young's modulus of rubber is $10^4 \ N/m^2$ and the area of cross-section is $2 \ cm^2$. If a force of $2 \times 10^5 \ dynes$ is applied along its length,then its initial length $L$ becomes:

Two wires $A$ and $B$ of same length, same radius and same Young's modulus are heated to the same range of temperatures. If the coefficient of linear expansion of $A$ is $\frac{3}{2}$ times that of $B$, then the ratio of the thermal stresses produced in the two wires $A$ and $B$ is

Two wires $A$ and $B$ are of the same material. Their lengths are in the ratio $1: 2$ and diameters are in the ratio $2: 1$. When stretched by forces $F_{A}$ and $F_{B}$ respectively,they get equal increase in their lengths. Then the ratio $F_{A} / F_{B}$ is

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 $Y = 2 \times 10^{11} \, N/m^2$)