A particle moves in a circle of radius 25cm at two revolutions per second. The radial acceleration of the particle is:
Correct answer: C. 4π2
- A. π2
- B. 8π2
- C. 4π2
- D. Zero
Explanation
The correct answer is option C: 4π². The radial acceleration can be calculated by converting the number of revolutions per second to radians per second to find the angular velocity (ω), and then using the formula a = ω²r with the given radius of 25 cm. The calculated radial acceleration is approximately 4π² m/s².Since, n = 2,ω = 2π × 2 = 4π rad/s²So acceleration = ω²r= (4π)² × 25/100 m/s² = 4π²Options A, B, and D are incorrect as they provide values that do not align with the correct formula and calculations involved in determining the radial acceleration of the particle.
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Rotational motion relates angular displacement, angular velocity and angular acceleration to linear displacement, tangential velocity and tangential acceleration through the radius. Questions use radians, v equals r omega and tangential acceleration, while distinguishing tangential velocity from centripetal acceleration and angular quantities from their linear counterparts.
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