$A$ force $F$ is applied on a wire of radius $r$ and length $L$,and the change in the length of the wire is $l$. If the same force $F$ is applied on a wire of the same material with radius $2r$ and length $2L$,then what is the change in the length of the second wire?

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:

There is some change in length when a $33000 \,N$ tensile force is applied on a steel rod of area of cross-section $10^{-3} \,m^2$. The change of temperature required to produce the same elongation, if the steel rod is heated, is (The modulus of elasticity is $3 \times 10^{11} \,N/m^2$ and the coefficient of linear expansion of steel is $1.1 \times 10^{-5} /{ }^{\circ}C$). (in $^{\circ}C$)

The Young's modulus of a wire of length $L$ and radius $r$ is $Y$. If the length is reduced to $\frac{L}{2}$ and radius is $\frac{r}{2}$,then the Young's modulus will be

If the ratio of diameters,lengths and Young's moduli of steel and brass wires shown in the figure are $p, q$ and $r$ respectively,then the corresponding ratio of increase in their lengths would be

Two metallic wires $P$ and $Q$ have the same volume and are made up of the same material. If their areas of cross-section are in the ratio $4:1$ and a force $F_1$ is applied to $P$,an extension of $\Delta l$ is produced. The force required to produce the same extension in $Q$ is $F_2$. The value of $\frac{F_1}{F_2}$ is . . . . . . .