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A particle moves on a circular path of radius 4 m. At one instant its speed is 20 m/s and its total acceleration makes an angle of 37 deg with the line drawn from the particle toward the centre. (i) At what rate is its speed increasing? (ii) What is the magnitude of its total acceleration?

1. (i) 15 m/s² (ii) 25 m/s²
2. (i) 12 m/s² (ii) 20 m/s²
3. (i) 10 m/s² (ii) 20 m/s²
4. (i) 8 m/s² (ii) 16 m/s²

Correct answer: (i) 15 m/s² (ii) 25 m/s²

Solution

a_c = v²/R = 400/4 = 20 m/s². The acceleration makes 37 deg with the radial direction, so aₜ = a_c tan 37 = 20*(3/4) = 15 m/s² (rate of speed increase), and total a = a_c/cos 37 = 20/0.8 = 25 m/s².

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