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A uniform circular disc of radius 50 cm at rest is free to turn about an axis which is perpendicular to its plane and passes through its centre. It is subjected to a torque which produces a constant angular acceleration of 2.0 rad s⁻². Its net acceleration in ms⁻² at the end of 2.0s is approximately:

1. 8.0
2. 7.0
3. 6.0
4. 3.0

Correct answer: 8.0

Solution

The net acceleration is the vector sum of tangential acceleration and centripetal acceleration. Tangential acceleration is given by αr = 2 × 0.5 = 1 m/s². After 2 seconds, angular velocity ω = αt = 2 × 2 = 4 rad/s. Centripetal acceleration is ω²r = 4² × 0.5 = 8 m/s². Net acceleration = √(1² + 8²) ≈ 8.0 m/s².

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