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 __________.
Question
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