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A stone attached to the end of a 1 m long string is moved in a horizontal circle at constant speed. If it completes 22 revolutions in 44 s, what is the magnitude of its acceleration?

1. π² m s⁻² and directed along the radius toward the centre
2. π² m s⁻² and directed along the radius away from the centre
3. π² m s⁻² and directed tangentially to the circle
4. π²/4 m s⁻² and directed along the radius toward the centre

Correct answer: π² m s⁻² and directed along the radius toward the centre

Solution

22 rev in 44 s gives T = 2 s, so w = 2*pi/T = pi rad/s. Centripetal acceleration = w^2 r = pi^2 * 1 = pi^2 m/s^2, directed along the radius toward the centre.

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