Two uniform rods of equal lengths (l) and equal masses have coefficient of linear expansion α and 2α are placed in contact on a smooth horizontal surface as shown. The temperature of system is θ°C. Now the temperature is increased by Δθ°C. The junction of the rods will shift from its initial position by?

According to the law of thermal expansion, the change in length is linear function of change of temperature.
In this case, we will assume the junction temperature ans also, change in length wil be more towards the side, that is having greater value of thermal expansion.


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As the rods have the sam mass the COM is at junction so after heating it shifts to right side so write the COM Formula So shift in Com is ( -m(l/2 +α l/2 Δθ) + m(l/2 + 2α l/2 Δθ))/2m = lα Δθ/4