An Object is defined in the rules
a nonliving, distinct thing...
There is some debate about the action cost of dropping a Weapon; however, the set of Objects in general is larger than, and contains the subset of objects that are Weapons.
There are a number of overlapping complications to consider, since Improvised Weapons can be either objects or weapons at different times, in different contexts
An improvised weapon is an object wielded as a makeshift weapon...
And, it would be both odd and counterintuitive, to put special restrictions on weapons, as opposed to Objects unless there was an exception to the general rules.
So, the general question then is, is it free to drop an Object in general, e.g. a spellbook?