There are two uses of whose:
- Relative whose, used in forming relative clauses.
- Interrogative whose, used in asking a question.
The former can refer to inanimate objects, but the latter cannot.
Take a look at this sentence, in which relative whose refers to an inanimate object:
Two of these were large marble jars whose manufacture must have represented an enormous amount of work since metal tools were unknown at that time. (source)
Here, relative whose refers back to the noun phrase large marble jars, an inanimate object. This usage is fairly common and unremarkable.
However, interrogative whose does not have this ability. If you wanted to ask which cars had engines that needed replacing, this sentence would be unacceptable:
*Whose engines need replacing?
This is because interrogative whose cannot refer back to cars, an inanimate object.
Huddleston and Pullum use the labels personal and non-personal for this distinction. In these terms, interrogative whose is personal, and relative whose can be either personal or non-personal.
In this answer, * marks a sentence as unacceptable.