Answer
When we jerk paper, enough momentum is changed in a very short time, hence large force is applied on the paper towel. So, tearing of the paper towel occurs.
More paper on the roll means more moment of inertia and so rolling would be difficult and tearing would be easy. Meanwhile, less paper on the roll means less moment of inertia, so rolling would be easy and tearing will be difficult.
Hence, we conclude that amount of paper on the roll will affect the result.
Work Step by Step
When we jerk paper, enough momentum is changed in a very short time, hence large force is applied on the paper towel. So, tearing of the paper towel occurs.
More paper on the roll means more moment of inertia and so rolling would be difficult and tearing would be easy. Meanwhile, less paper on the roll means less moment of inertia, so rolling would be easy and tearing will be difficult.
Hence, we conclude that amount of paper on the roll will affect the result.