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
