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The part of the sentence "the objects within" is correct and usable in written English.
You can use it to refer to the objects that are included within a certain area, such as a room or building. For example: "The objects within the room were scattered across the floor."
Exact(57)
Here, Cesar Luna, pictured at right, presides over the carts and the objects within them.
As long as the objects within the room remain stationary, the reflected beam remains the same as the broadcast beam.
Light bounces off the door, scatters into the room, hits the objects within and then bounces back to the detector.
The camera acquired images of the room and translated them into patterns of vibration, which represented the physical space of the room and the objects within it.
A set designer may construct the perfect room, but if the objects within it don't radiate the personality of the people whose lives have formed it, the film won't ring true.
"I'm constantly editing, eliminating, adding, altering my space and the objects within it until it starts to reflect what I'd like the image of myself to be and the kind of space I envision myself living in.
Ponti designed not only the 10,000-square-foot, six-bedroom house, but all the furniture and many of the objects within it with the spirit and sensuality that were the hallmarks of his humanistic brand of modernism.
Because virtual reality encompasses both the space we inhabit and the objects within that space, artists can conjure almost limitless expanses and enormous shifts in scale impossible in a world of matter.
Similar(3)
MyStuff provides areas in which to enter information on an object's history, condition and location, and allows the user to import a digital image of the object within the listing.
Formal role: it distinguishes the object within a larger domain (what it is).
The derived CPF data is used to start laser ranging ('chase' the object) within the same pass to retrieve highly accurate distance information.
More suggestions(4)
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com