An aluminium and steel rods having same lengths and cross-sections are joined to make total length of 120 cm at 30°C. The coefficient of linear expansion of aluminium and steel are $$24\times10^{-6}/^{\circ}C\text{ and }1.2\times10^{-5}/^{\circ}C$$, respectively. The length of this composite rod when its temperature is raised to $$100^\circ$$ C, is ___ cm.

Two rods each of length 60 cm at 30°C. Al: $$\alpha_1 = 24 \times 10^{-6}$$, Steel: $$\alpha_2 = 12 \times 10^{-6}$$.

Temperature rise = 70°C.

Change in Al length: $$60 \times 24 \times 10^{-6} \times 70 = 60 \times 1680 \times 10^{-6} = 0.1008$$ cm

Change in Steel length: $$60 \times 12 \times 10^{-6} \times 70 = 60 \times 840 \times 10^{-6} = 0.0504$$ cm

Total change = 0.1008 + 0.0504 = 0.1512 cm ≈ 0.15 cm

New length = 120.15 cm.

The answer is Option 3: 120.15 cm.