$5 \,m$ 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 be (in $mm$):

$A$ $3 \ m$ long wire of radius $3 \ mm$ shows an extension of $0.1 \ mm$ when loaded vertically by a mass of $50 \ kg$ in an experiment to determine Young's modulus. The value of Young's modulus of the wire as per this experiment is $P \times 10^{11} \ Nm^{-2}$,where the value of $P$ is: (Take $g = 3 \pi \ m/s^2$)

Two wires $A$ and $B$ made of the same material and areas of cross-section in the ratio $1: 2$ are stretched by the same force. If the masses of the wires $A$ and $B$ are in the ratio $2: 3$,then the ratio of the elongations of the wires $A$ and $B$ is

Steel and copper wires of the same length are stretched by the same weight one after the other. The Young's modulus of steel and copper are $2 \times 10^{11} \, N/m^2$ and $1.2 \times 10^{11} \, N/m^2$,respectively. What is the ratio of the increase in their lengths?

Two similar wires under the same load yield elongations of $0.1 \ mm$ and $0.05 \ mm$ respectively. If the area of cross-section of the first wire is $4 \ mm^2$,then the area of cross-section of the second wire is..... $mm^2$.

Two wires $A$ and $B$ are made of the same material. Their diameters are in the ratio of $1: 2$ and their lengths are in the ratio of $1: 3$. If they are stretched by the same force,then the increase in their lengths will be in the ratio of: