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

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Q: 125 (IAS/2004)
A spherical body moves with a uniform angular velocity x around a circular path of radius r.
Which one of the following statements is correct?

question_subject: 

Science

question_exam: 

IAS

stats: 

0,21,38,18,21,13,7

keywords: 

{'radial acceleration': [0, 0, 1, 0], 'spherical body': [0, 0, 1, 0], 'uniform angular velocity': [0, 0, 1, 0], 'circular path': [0, 0, 1, 2], 'acceleration': [0, 0, 2, 8], 'body': [27, 3, 23, 37], 'path': [1, 0, 4, 2]}

The correct answer is option 2: `The body has a radial acceleration x^2.r directed towards the centre of the path.` this option can be understood as follows:

Option 1: `The body has no acceleration`: This statement is incorrect. When a body moves with uniform angular velocity in a circular path, it experiences radial (centripetal) acceleration towards the center of the path.

Option 2: `The body has a radial acceleration x^2.r directed towards the centre of the path`: This statement is correct. The equation for centripetal acceleration is a = rω^2 (where ω is the angular velocity and r is the radius). Thus, the acceleration is x^2.r directed towards the center of the circular path.

Option 3: `The body has a radial acceleration 2/5.x^2.r directed away from the centre of the path`: This statement is incorrect because the acceleration is directed towards the center, not away from it.

Option 4: `The body has an acceleration x^2.r tangential to its path`: This statement is also incorrect because the acceleration due to uniform circular motion is always directed towards the center of the circle, not tangential to it.