Answer:
The temperature at which the wing would be shorter is [tex]- 80.69^{\circ}C[/tex]
Solution:
The original length of the Aluminium wing, [tex]l_{w} = 25 m[/tex]
Temperature, T = [tex]21^{\circ}C[/tex]
Change in the wing's length, [tex]\Delta l_{w} = 0.06 m[/tex]
Also, for Aluminium, at temperature between [tex]20^{\circ}C[/tex] to [tex]100^{\circ}C[/tex], the linear expansion coefficient, [tex]\alpha = 23.6\times 10^{- 6}/^{\circ}C[/tex]
Now, Change in length is given by:
[tex]\Delta l_{w} = l_{w}\alpha \Delta T[/tex]
[tex]0.06 = 25\times 23.6\times 10^{- 6}\(T - T')[/tex]
[tex]\frac{0.06}{5.9\times 10^{- 4}} = 21^{\circ}C _ T'[/tex]
[tex]T' = - 80.69^{\circ}C[/tex]
