If the ratio of the masses of wires of the same material is $1 : 3 : 5$ and the ratio of their lengths is $5 : 3 : 1$,what is the ratio of their resistances?

$A$ certain wire has a resistance $R$. The resistance of another wire identical with the first except having twice its diameter is (in $,R$)

Two wires of equal length,one of aluminium and the other of copper,have the same resistance. Which of the two wires is lighter? Hence,explain why aluminium wires are preferred for overhead power cables. $(\rho_{Al} = 2.63 \times 10^{-8} \; \Omega m, \rho_{Cu} = 1.72 \times 10^{-8} \; \Omega m, \text{Relative density of } Al = 2.7, \text{of } Cu = 8.9.)$

The resistance of the bulb filament is $100 \ \Omega$ at a temperature of $100^{\circ} C$. If its temperature coefficient of resistance is $0.005 \ ^{\circ} C^{-1}$,at what temperature will its resistance become $200 \ \Omega$ (in $^{\circ} C$)?

The length of a hollow tube is $5\,m$,its outer diameter is $10\,cm$,and the thickness of its wall is $5\,mm$. If the resistivity of the material of the tube is $1.7 \times 10^{-8} \,\Omega m$,then the resistance of the tube will be:

$A$ wire $50\, cm$ long and $1\, mm^2$ in cross-section carries a current of $4\, A$ when connected to a $2\, V$ battery. The resistivity of the wire is: