UPSC Prelims 2004·GS1·science-and-technology·science and technology

A spherical body moves with a uniform angular velocity around a circular path of radius r. Which one of the following statements is correct?

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  1. AThe body has no acceleration
  2. BThe body has a radial acceleration 2r directed towards the centre of the path.Correct
  3. CThe body has a radial acceleration 2/5 2r directed away from the centre of the path.
  4. DThe body has an acceleration 2r tangential to its path

Explanation

When a body moves in a uniform circular motion, its speed remains constant, but its direction changes continuously. This change in direction generates an acceleration directed toward the center of the circle, known as centripetal or radial acceleration. The formula for radial acceleration is the square of the angular velocity multiplied by the radius. In mathematical terms, if omega is the angular velocity and r is the radius, the acceleration is omega squared times r. Option B is the correct choice because it identifies that the body possesses a radial acceleration directed toward the center of the path. Although the provided text in the option uses the notation 2r, it represents the standard physics principle that uniform circular motion always involves a center-seeking acceleration. Options suggesting no acceleration, outward acceleration, or tangential acceleration are incorrect because uniform circular motion requires a constant inward force to maintain the curved path.
science-and-technology: A spherical body moves with a uniform angular velocity around a circular path of radius r. Which one of the following st

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