UPSC Prelims 2004 Q125: Science & Technology – Physics
A spherical body moves with a uniform angular velocity ω around a circular path of radius
r.
Which one of the following statements is correct?
- (a) The body has no acceleration
- (b) The body has a radial acceleration ω²r directed towards the centre of the path
- (c) The body has a radial acceleration 2/5 ω²r directed away from the centre of the path
- (d) The body has an acceleration ω²r tangential to its path
Answer: (b) The body has a radial acceleration ω²r directed towards the centre of the path
Explanation
Uniform circular motion
| Quantity | Value |
|---|---|
| Speed | Constant, v = w r |
| Acceleration | Centripetal, magnitude w^2 r, directed towards the centre |
| Tangential acceleration | Zero for uniform angular velocity |
A body moving with uniform angular velocity w on a circle of radius r has a radial acceleration of w^2 r directed towards the centre.
Answer: (b) The body has a radial acceleration w^2 r directed towards the centre of the path.
Why each option is right or wrong
- (a) Incorrect. A body in circular motion is always accelerating.
- (b) CORRECT. Centripetal acceleration is w^2 r towards the centre.
- (c) Incorrect. The acceleration points towards the centre, not away from it.
- (d) Incorrect. The tangential acceleration is zero for uniform angular velocity.
Key point
Centripetal acceleration a = v^2 / r = w^2 r, always towards the centre.
Remember
Uniform circular motion has centripetal acceleration w^2 r.
Common mistakes
- Saying uniform motion means no acceleration.
- Directing the acceleration outwards (centrifugal).
- Mixing tangential and radial acceleration.
Exam tip
Uniform speed does not mean zero acceleration in a circle.
Sources
- NCERT Class XI Physics — Motion in a Plane
- NCERT Class XI Physics — Laws of Motion (circular motion)