A spherical body moves with a uniform angular velocity 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 2r directed towards the centre of the path.
C
The body has a radial acceleration 2/5 2r directed away from the centre of the path.
D
The body has an acceleration 2r tangential to its path
Correct Answer: Option B
Explanation
1. A spherical body moves with a uniform angular velocity (ω) around a circular path of radius r.
2. Uniform angular velocity means the speed of the body (v = ωr) is constant, but its direction is continuously changing as it moves in a circle.
3. Because the direction of velocity is changing, the body must have an acceleration. Therefore, statement (A) is incorrect.
4. This acceleration is directed towards the centre of the circular path and is called centripetal acceleration (or radial acceleration).
5. The magnitude of the centripetal acceleration is given by a = v²/r or a = ω²r.
6. Statement (B) says the body has a radial acceleration ω²r directed towards the centre. This matches the definition and formula for centripetal acceleration. So, statement (B) is correct.
7. Statement (C) gives the wrong magnitude and direction (away from centre).
8. Statement (D) describes tangential acceleration, which is zero for uniform circular motion (constant speed).
Therefore, the correct statement is (B).