$A$ $5\, m$ 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 Young's modulus of a wire of length $L$ and radius $r$ is $Y \, N/m^2$. What will be the Young's modulus of a wire made of the same material with length $L/2$ and radius $r/2$?

The dimensional formula for Young's modulus is

$A$ rigid bar of mass $15\; kg$ is supported symmetrically by three wires each $2.0\; m$ long. Those at each end are of copper and the middle one is of iron. Determine the ratio of their diameters if each is to have the same tension.

$A$ wire of cross-sectional area $A$,modulus of elasticity $2 \times 10^{11} \text{ N m}^{-2}$,and length $2L = 2 \text{ m}$ is stretched between two vertical rigid supports. When a mass of $2 \text{ kg}$ is suspended at the middle,it sags from its original position,making an angle $\theta = \frac{1}{100} \text{ radian}$ with the horizontal at the points of support. The value of $A$ is . . . . . . $\times 10^{-4} \text{ m}^2$. (Given: $g = 10 \text{ m/s}^2$)

One end of a steel wire of radius $r$ is fixed to a ceiling and a load of $3 \ kg$ is attached to the free end of the wire. Another wire made of copper of radius $2r$ is attached to the bottom of the $3 \ kg$ load and a $2 \ kg$ load is attached to the free end of the copper wire. The ratio of longitudinal strains produced in copper and steel wires is (Young modulus of steel $= 20 \times 10^{10} \ Nm^{-2}$,Young modulus of copper $= 12 \times 10^{10} \ Nm^{-2}$)