UPSC Prelims 2004 · General Studies

Question 125: Science and Technology

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?

aThe body has no acceleration

bThe body has a radial acceleration ω²r directed towards the centre of the path

cThe body has a radial acceleration 2/5 ω²r directed away from the centre of the path

dThe body has an acceleration ω²r tangential to its path

AnswerThe answer is (b).

A body moving in a circle at uniform angular velocity changes direction constantly, so it is accelerating, even though its speed is constant. The acceleration is centripetal: of magnitude ω²r (equal to v²/r), directed towards the centre. The 2/5 factor in (c) belongs to the moment of inertia of a solid sphere, not to this motion.

Why each option is right or wrong

(a) The direction of velocity keeps changing, so there is acceleration.
(b) Correct: the centripetal acceleration is ω²r towards the centre.
(c) The acceleration points towards the centre, not away, and has no 2/5 factor.
(d) The acceleration is radial, not tangential, for uniform motion.

Explanation: written by UPSC Grade, not by UPSC.

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Source: UPSC, Civil Services (Preliminary) Examination 2004, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.