Heat, temperature and thermal expansion

A metallic bar of Young's modulus, \(0.5\times10^{11}\) N m\(^{-2}\) and coefficient of linear thermal expansion \(10^{-5}\,{}^\circ\)C\(^{-1}\), length 1 m and area of cross-section \(10^{-3}\) m\(^2\) is heated from \(0^\circ\)C to \(100^\circ\)C without expansion or bending. The compressive force developed in it is:

A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is : (\(\alpha_{Cu} = 1.7\times10^{-5}\) K\(^{-1}\) and \(\alpha_{Al} = 2.2\times10^{-5}\) K\(^{-1}\))

Coefficient of linear expansion of brass and steel rods are \(\alpha_1\) and \(\alpha_2\). Lengths of brass and steel rods are \(l_1\) and \(l_2\) respectively. If \((l_2 - l_1)\) is maintained same at all temperatures, which one of the following relations holds good ?