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A particle starting from rest, moves in a circle of radius ‘r’. It attains a velocity of V₀ m/s in the nth round. Its angular acceleration will be:

1. V₀² / 4πnr rad/s²
2. V₀ / nr rad/s²
3. V₀² / 2πnr² rad/s²
4. V₀² / 4πnr² rad/s²

Correct answer: V₀² / 4πnr rad/s²

Solution

The angular acceleration (α) is given by the change in angular velocity (ω) over time. The angular velocity after n rounds is ω = V₀ / r. The total angle covered in n rounds is θ = 2πn. Using the equation ω² = 2αθ, substituting ω and θ, and solving for α gives α = V₀² / (4πnr).

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