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Question: Answered & Verified by Expert
A solid body rotates about a stationary axis so that its angular velocity depends on the rotational angle ϕ as ω=ω0-kϕ where ω0 and k are positive constants. At the moment t=0, ϕ=0, find the time dependence of rotation angle
PhysicsLaws of MotionJEE Main
Options:
  • A kω0 e-kt
  • B ω0k e-kt
  • C ω0k 1-e-kt
  • D kω0 e-kt-1
Solution:
2226 Upvotes Verified Answer
The correct answer is: ω0k 1-e-kt
ω=ω0-kϕ or dϕdt=ω0-kϕ

Or 0ϕdϕω0-kϕ= 0tdt

Or -1k lnω0-kϕ0ϕ=t

Or lnω0-kϕω0= -kt

ϕ=ω0k 1-e-kt

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