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Q.

A particle of mass m moves along a circular path of radius r with a centripetal acceleration an changing with time t as an=kt2, where k is a positive constant. The average power developed by all the forces acting on the particle during the first t0 seconds is

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a

mkrt0

b

mkrt022

c

mkrt02

d

mkrt04

answer is C.

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Detailed Solution

Given an=kt2 or v2r=kt2 or v2=krt2Therefore, average power delivered = Total work done  Total time elapsed or  

=12mv2−02t0=m2krt02t0=mkrt02Alternative: v=krt⇒at=krP=Ftv=matv=mkrt⟨P⟩=∫0t0 Pdtt0=12mkrt0

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