Answer:
0.65 m/s
Explanation:
Potential energy = Kinetic energy + Potential energy
m₁gh = ½ m₁v² + ½ m₂v² + ½ Iω² + m₂gh
(m₁ − m₂)gh = ½ m₁v² + ½ m₂v² + ½ Iω²
2(m₁ − m₂)gh = m₁v² + m₂v² + Iω²
For a solid disk, I = ½ Mr². Assuming no slipping, ω = v/r.
2(m₁ − m₂)gh = m₁v² + m₂v² + (½ Mr²) (v/r)²
2(m₁ − m₂)gh = m₁v² + m₂v² + ½ Mv²
4(m₁ − m₂)gh = 2m₁v² + 2m₂v² + Mv²
4(m₁ − m₂)gh = (2m₁ + 2m₂ + M) v²
v² = 4(m₁ − m₂)gh / (2m₁ + 2m₂ + M)
v² = 4 (0.25 kg − 0.20 kg) (9.8 m/s²) (0.30 m) / (2 × 0.25 kg + 2 × 0.20 kg + 0.50 kg)
v² = 0.42 m²/s²
v = 0.65 m/s