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Q.

A solid body rotates about a stationary axis so that its angular velocity depends upon the rotation angle θ as ω=ω0-kθ, where ω0and k are positive constants. At the moment t =0, the angle θ= 0. Which of the following variations are correct?

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a

b

c

d

answer is A.

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Detailed Solution

ω=ω0−kθ​⇒dθdt=ω0−kθ​∴∫0θdθω0−kθ=∫0tdt​⇒−1klnω0−kθω0=t​∴θ=ω0k1−e−kt​⇒ω=dθdt=ω0e−kt
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