Two particles, A and B, are in uniform circular motion about a common center. The acceleration of particle A is 8.6 times that of particle B

Question

Two particles, A and B, are in uniform circular motion about a common center. The acceleration of particle A is 8.6 times that of particle B. The period of particle B is 2.2 times the period of particle A. The ratio of the radius of the motion of particle A to that of particle B is closest to __________.

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Thiên Ân 4 years 2021-08-28T00:50:35+00:00 1 Answers 9 views 0

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  1. MichaelMet
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    2021-08-28T00:52:22+00:00
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    Answer:

    Explanation:

    1.78

    Explanation:

    The centripetal acceleration of particle, A is a₁ = r₁ω₁² = r₁(2π/T₁)² = 4π²r₁/T₁²

    The centripetal acceleration of particle, B is a₂ = r₂ω₂² = r₂(2π/T₂)² = 4πr₂/T₂². Where r₁, r₂ and T₁, T₂ are the radii and periods of particles A and B respectively.

    Given that a₁ = 8.6a₂ and T₂ = 2.2T₁, ⇒ a₁/a₂ = 8.6 and T₁/T₂ = 1/2.2

    a₁/a₂ = 8.6 = 4π²r₁/T₁² ÷ 4πr₂/T₂² = r₁/r₂(T₂/T₁)²

    ⇒ r₁/r₂ = a₁/a₂(T₁/T₂)² = 8.6 / 2.2² =   1.78.

    So, the ratio of the radius of the motion of particle A to that of particle B is closest to 1.78

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