Two particles,A and B,are in uniform circular motion about a common center.The acceleration of particle A is 4.7 times that of particle B.Particle B takes 2.4 times as long for a rotation as particle A.The ratio of the radius of the motion of particle A to that of particle B is closest to:
A)0.82
B)2.0
C)3.8
D)0.51
E)11

Question

Quizplus · Accepted Answer

Let's denote the radius of the circular motion of particle A by r and that of particle B by s. Let the velocities of A and B be denoted by v and u, respectively. 
The acceleration of a particle in uniform circular motion is given by a = v^2/r.
We are given that a_A = 4.7a_B, which means that v_A^2/r = 4.7v_B^2/s. 
We are also given that B takes 2.4 times as long as A for one rotation. This implies that B travels around its circle 2.4 times for every time A travels around its circle once. Therefore, the ratio of their respective velocities is v/u = s/r * 2.4 (since they both cover the same angle in their respective circles in the same amount of time).
We can solve for v_A^2/v_B^2 and v/u in terms of r/s, and then equate the two expressions to get the ratio of r/s. After simplifying, we get:
r/s = (4.7 * 2.4)^1/3 ≈ 0.82, which is closest to choice A.

Two Particles,A and B,are in Uniform Circular Motion About a Common