Yes. Objects take damage from falling.
How much is up to the DM
Determining the amount of damage for falling objects is explicitly DM fiat per Dungeon Master Guide (DMG p247).
You might decide that some damage types are more effective against a particular object or substance than others.
The falling damage in the rules is specifically about creatures.
It would be reasonable to have falling damage per distance determined by an object's size, material, or other characteristics.
Use Damage Thresholds for damage susceptibility
Some objects are more susceptible to damage types than others. Considering using kind of damage reduction applied to components of sailing ships as a method for calculating damage to objects.
Damage Threshold from Ghosts of Saltmarsh (p. 186) or DMG (p. 247)
A component has immunity to all damage unless it takes an amount of damage that equals or exceeds its threshold, in which case it takes damage as normal. Damage that fails to bypass the threshold is considered superficial and does not reduce the component's hit points.
E.g. It would be fair to determine a chandelier has a damage threshold of 0 while a cannon ball has a damage threshold of 50.
Modeling driven vs story driven
D&D is not a good physics model
Calculating the results of statistics and rolls is running an engine. Doing that pauses the development of the story to determine an outcome, and the determination of the outcome by rolls might not be very satisfactory. It has been said by Jeremy Crawford and reiterated here that:
Indeed. D&D is not a physics engine.
Driving the story
Determining if an object is broken, unusable, repairable, or unaffected by a drop does not need to include the randomness of dice rolling, unless that's fun for your players.
When an object falls, consider:
- What outcome is expected by the players? Use surprise judiciously.
- What outcome drives the story they're interested in telling and participating in?
- Is it important or something that provides depth the the narrative?
It may become obvious that there are many cases where the dice can remain at rest and not break up the storytelling.