Two particles, A and B, are in uniform circular motion about a common center. The acceleration of particle A is 8.5 times that of particle B. The period of particle B is 2.0 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
A) rA/rB = 2.1.
B) rA/rB = 4.3.
C) rA/rB = 18.
D) rA/rB = 0.24.
E) rA/rB = 17.

Question

Quizplus · Accepted Answer

The acceleration of a particle in uniform circular motion is given by a = v^2/r, where v is the speed of the particle and r is the radius of the motion. The period of a particle in uniform circular motion is given by T = 2πr/v.Since the acceleration of particle A is 8.5 times that of particle B, we have:a_A = 8.5a_Bv_A^2/r_A = 8.5v_B^2/r_BSince the period of particle B is 2.0 times the period of particle A, we have:T_B = 2T_A2πr_B/v_B = 2(2πr_A/v_A)r_B/v_B = r_A/v_ASubstituting this into the first equation, we get:v_A^2/r_A = 8.5v_B^2/r_Bv_A^2/r_A = 8.5(v_A^2/r_A)1 = 8.5r_A/r_B = 1/8.5 = 0.118The closest answer choice is D) rA/rB = 0.24.

Two Particles, a and B, Are in Uniform Circular Motion