Two identical rods A and B are of equal lengths and at the...

Two identical rods $A$ and $B$ are of equal lengths and at the same temperature. The rod $A$ is placed at smooth surface but $B$ is placed at rough surface. If the temperature of both are raised by the same amount, then : (a) final length of $A$ is greater than that of $B$ (b) final length of both are same (c) final length of $A$ is lesser than that of $B$ (d) none of the above

Two identical rods $A$ and $B$ are of equal lengths and at the same temperature. The rod $A$ is placed at smooth surface but $B$ is placed at rough surface. If the temperature of both are raised by the same amount, then :
(a) final length of $A$ is greater than that of $B$
(b) final length of both are same
(c) final length of $A$ is lesser than that of $B$
(d) none of the above

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Key Concepts

Thermal Expansion

Thermal expansion is the phenomenon where materials increase in size as their temperature rises. This increase in length, area, or volume occurs because the atoms or molecules vibrate more vigorously and tend to move apart. The degree to which a material expands is quantified by its coefficient of thermal expansion, which is intrinsic to the material.

Boundary Conditions in Thermal Expansion

The way a material expands upon heating can be significantly affected by its external constraints or boundary conditions. When an object is free to move, it can expand uniformly in response to temperature changes. However, if the object is fixed or restrained in any way, its expansion may be limited or redirected, and additional stresses can develop within it.

Friction as a Constraint

Friction acting on a material can serve as a constraint by restricting its movement. If a material is in contact with a rough surface, friction can inhibit free expansion, leading to differences in the effective thermal expansion compared to when the material is resting on a frictionless surface. This constraint can result in a smaller observable change in dimensions such as length.

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