Conical Pendulum — RadiusMediumQuestion 30624
Question
A conical pendulum (string length L = 0.5 m) rotates at 4 rad/s. The cone half-angle θ satisfies:
- Acosθ = g/(ω²L) = 10/(16×0.5) = 1.25
- Bcosθ = g/(ω²L) = 1.25 → impossible; θ is undefined for this ωCorrect
- Ccosθ = 0.8, θ ≈ 37°
- Dcosθ = 0.5, θ = 60°
Correct answer
cosθ = g/(ω²L) = 1.25 → impossible; θ is undefined for this ω
Explanation
From conical pendulum: cosθ = g/(ω²L) = 10/(16×0.5) = 10/8 = 1.25. Since cosθ > 1 is impossible, the string cannot make a conical pendulum at ω = 4 rad/s with L = 0.5 m — it would require ω > √(g/L) = √20 ≈ 4.47 rad/s.