The elongation of the copper wire of cross-sectional area $3.5 \,mm^2$, as shown in the figure, is (Given: $Y_{\text{copper}} = 10 \times 10^{10} \,N/m^2$ and $g = 10 \,m/s^2$).

$A$ wire of length $L$ and radius $r$ is clamped rigidly at one end. When the other end of the wire is pulled by a force $F$,its length increases by $5\,cm$. Another wire of the same material of length $4L$ and radius $4r$ is pulled by a force $4F$ under the same conditions. The increase in length of this wire is $....cm$.

$A$ horizontal steel railroad track has a length of $100 \, m$ when the temperature is $25^{\circ} C$. The track is constrained from expanding or bending. The stress on the track on a hot summer day,when the temperature is $40^{\circ} C$,is ............. $\times 10^7 \, Pa$. (Note: The linear coefficient of thermal expansion for steel is $1.1 \times 10^{-5} /^{\circ} C$ and the Young's modulus of steel is $2 \times 10^{11} \, Pa$.)

$A$ wire of length $L$ and radius $r$ is rigidly fixed at one end. On stretching the other end of the wire with a force $F$,the increase in its length is $l$. If another wire of same material but of length $2L$ and radius $2r$ is stretched with a force of $2F$,the increase in its length will be

Two wires are made of the same material and have the same volume. The first wire has cross-sectional area $A$ and the second wire has cross-sectional area $3A$. If the length of the first wire is increased by $\Delta l$ on applying a force $F$,how much force is needed to stretch the second wire by the same amount?

$A$ wire of length $L$ and radius $r$ is clamped at one end. If its other end is pulled by a force $F$,its length increases by $l$. If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant,the increase in length will become.