The Young's modulus of a rubber string $8\, cm$ long and density $1.5\, kg/m^3$ is $5 \times 10^8\, N/m^2$. If it is suspended from the ceiling in a room,the increase in length due to its own weight will be:

$A$ cable is cut to half of its original length. What will be the effect on the increase in its length under a given load?

$A$ wire of area of cross-section $10^{-6} \ m^2$ is increased in length by $0.1 \%$. The tension produced is $1000 \ N$. The Young's modulus of the wire is:

The Young's modulus of a wire is $Y$. If the energy per unit volume is $E$,then the strain will be

The decrease in length of a metal bar of length $L$ and cross-sectional area $A$ when compressed with a load $F$ along its length is (where $Y$ is Young's modulus of the material of the metal bar).

Two metal wires $A$ and $B$ have lengths $L$ and $3L$ respectively. The radii of the cross-sectional circular areas of wires $A$ and $B$ are $R$ and $2R$, respectively. These wires are joined end-to-end along their axis. When one end of the combined system is fixed and the other end is pulled with a constant force $F$, the elongation in both wires is equal. If $Y_A$ and $Y_B$ are the Young's moduli of wires $A$ and $B$, respectively, then the ratio $Y_B / Y_A$ is: