Question

A particle of mass m moves in a circular path of radius r, under the action force which delivers it constant power p and increases it's speed. The angular acceleration of particle at time(t) is proportional

(1). 1/√t
(2). √t
(3). t^0
(4). t^3/2

Please answer it correctly an briefly.

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Answer 1

Here, the only work done is in the direction of motion which causes acceleration. Power, p= Force × Speed in direction of force = Mass × acceleration × speed =m×dvdt×v where, dvdt= Linear acceleration. vdvdt=pm[p is constant ] Integrating, 12v2=(pm)×t 12(rω)2=(pm)×t or ω2=2pmr2×t or w=2pmr2×t−−−−−−√ =ct1/2 where, c=con stant Thus, the angular acceleration is dωdt=12ct−1/2 i. e. angular acceleration is proportional to t−1/2 or 1t√.

Answer 2

Answer:

t - 1/2 .............................