Question Detail
Question
What is the period of revolution for a conical pendulum with a string of length L making an angle θ with the vertical? (Hint: v = 2πr/T, and tan θ = v²/gr)
Correct Answer
Option B is the correct answer.
Detailed Explanation
We have tan θ = v²/(gr). Also, v = 2πr/T, so v² = 4π²r²/T². Substitute: tan θ = (4π²r²)/(T² g r) = 4π²r/(T² g). But r = L sin θ. So tan θ = 4π² (L sin θ) / (T² g). Since tan θ = sin θ / cos θ, we get sin θ / cos θ = 4π² L sin θ / (T² g). Canceling sin θ gives 1/cos θ = 4π² L / (T² g). Rearranging for T² gives T² = 4π² L cos θ / g, so T = 2π√(L cos θ / g).
Hint
This requires combining several formulas: tan θ = v²/gr, v = 2πr/T, and the geometric relationship r = L sin θ.