An object will not move if:
A.) All forces acting on it are balanced.
This can be proved by example, while similtaneously proving the other answers wrong.
Take for example;
Two people are pushing on a box with 30N, one person being on the right, the other being on the left.
The opposing forces are exerting against eachother, creating a stable position on the box.
How about "if there was no gravity on it"?
Take for example an airplane. Turbulence effects the plane even when it's defying gravity.
The next two are easy to debunk.
"It's mass increases"
This can be disproved by anything.
If I were to become bigger, I'm not moving, my body is just extending in size.
This also applies to weight.
The answer is A.)
I hope this helps!
