A $500 \mathrm{~g}$ ball is attached to one end of an aluminum wire of area of cross-section $0.5…
A $500 \mathrm{~g}$ ball is attached to one end of an aluminum wire of area of cross-section $0.5 \mathrm{~mm}^2$ and an unstretched length of $1.4 \mathrm{~m}$. The other end of the wire is fixed to the top of a vertical pole. The ball rotates about the pole in a horizontal plane such that the angle between the wire and the horizontal is $30^{\circ}$. The increase in the length of the wire is ____ $\mathrm{mm}$. (Young's modulus of aluminum $=0.7 \times 10^{11} \mathrm{Nm}^{-2}$ and acceleration due to gravity $=10 \mathrm{~ms}^{-2}$)