With a rise in temperature,the Young's modulus of elasticity

There are two wires of the same material and same length. If the diameter of the second wire is two times the diameter of the first wire,then the ratio of the extension produced in the wires by applying the same load will be:

$A$ brass wire $1.8\; m$ long at $27\;^{\circ}C$ is held taut with little tension between two rigid supports. If the wire is cooled to a temperature of $-39\;^{\circ}C$,what is the tension developed in the wire,if its diameter is $2.0\; mm$? (Coefficient of linear expansion of brass $\alpha = 2.0 \times 10^{-5}\; K^{-1}$; Young's modulus of brass $Y = 0.91 \times 10^{11}\; Pa$)

$A$ steel rod of radius $20 \ mm$ and length $2 \ m$ is acted upon by a force of $400 \ kN$ along its length. The values of stress and strain are respectively $(Y_{\text{steel}} = 2 \times 10^{11} \ N \ m^{-2})$.

$A$ steel ring of radius '$r$' is to be fitted over a wooden disc of radius '$R$' $(R > r)$. The force required to expand the ring so that it fits over the disc is ($Y =$ Young's modulus of steel,$A =$ area of cross-section of the wire).

$A$ rod of length $l$ and area of cross-section $A$ is heated from $0^{\circ}C$ to $100^{\circ}C$. The rod is so placed that it is not allowed to increase in length,then the force developed is proportional to