Question

Is the magnitude of the acceleration of the center of mass of spool A greater than, less than, or equal to the magnitude of the acceleration of the center of mass of spool B?

Answer 1

Answer:

The acceleration of the centre of mass of spool A is equal to the magnitude of the acceleration of the centre of mass of spool B.

Explanation:

From the image attached, the description from the complete question shows that the two spools are of equal masses (same weight due to same acceleration due to gravity), have the same inextensible wire with negligible mass is attached to both of them over a frictionless pulley; meaning that the tension in the wire is the same on both ends.

And for the acceleration of both spools, we mention the net force.

The net force acting on a body accelerates the body in the same direction as that in which the resultant is applied.

For this system, the net force on either spool is exactly the same in magnitude because the net force is a difference between the only two forces acting on the spools; the tension in the wire and their similar respective weights.

With the net force and mass, for each spool equal, from

ΣF = ma, we get that a = ΣF/m

Meaning that the acceleration of the identical spools is equal also.

Hope this Helps!