100 POINTS.
PLEASE EXPLAIN YOUR ANSWER.

Explanation:

Draw free body diagrams for each mass.

There are 3 forces on the disk: weight force mg pulling down, normal force N pushing up, and tension force T pulling right.

There are 2 forces on the cylinder: tension force T pulling up and weight force 3mg pulling down.

Sum of forces on the disk in the centripetal direction:

∑F = ma

T = m v²/r

Sum of forces on the cylinder in the vertical direction:

∑F = ma

T − 3mg = 0

T = 3mg

Substituting:

3mg = m v²/r

3gr = v²

v = √(3gr)

Plug in values:

v = √(3 × 10 m/s² × 0.800 m)

v = √24 m/s

v ≈ 4.90 m/s

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