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A $5\, m$ long aluminium wire ($Y = 7 \times {10^{10}}N/{m^2})$ of diameter $3\, mm$ supports a $40\, kg$ mass. In order to have the same elongation in a copper wire $(Y = 12 \times {10^{10}}N/{m^2})$ of the same length under the same weight, the diameter should now be, in $mm.$
The extension of a wire by the application of load is $3$ $mm.$ The extension in a wire of the same material and length but half the radius by the same load is..... $mm$
A uniform metal rod of $2\, mm^2$ cross section fixed between two walls is heated from $0\,^oC$ to $20\,^oC$. The coefficient of linear expansion of rod is $12\times10^{-6}/^oC$. Its Young's modulus of elasticity is $10^{11} \,N/m^2$. The energy stored per unit volume of rod will be ....... $J/m^3$
What must be the lengths of steel and copper rods at $0^o C$ for the difference in their lengths to be $10\,cm$ at any common temperature? $(\alpha_{steel}=1.2 \times {10^{-5}} \;^o C^{-1})$ and $(\alpha_{copper} = 1.8 \times 10^{-5} \;^o C^{-1})$