My question that i'm suppose the answer is: two particles, a and b, are in uniform circular motion about a common center. the acceleration of particle a is 6.0 times that of particle b. particle b takes 2.4 times as long for a rotation as particle a. what is the ratio of the radius of the motion of particle a to that of particle b?

the options are:

5: 1

1: 3

14: 1

1: 1

i'm very confused here because i don't understand how any of these choices can represent the answer. i know the acceleration of a is 6 times greater than b, and b takes 2.4 times longer to to complete a rotation compared to a. but how can i compare the motions, when it doesn't really give me anything to compare it to?

The ratio of the radius of the motion of particle A to that of particle B is 1:1

Solution:

Let v be the uniform circular motion,

centripetal acceleration be

On substituting 1 in 2 we get,  

Given, acceleration of A = 6x; B = x Time taken by A = t ; B = 2.4t For particle A, substituting the values,  

For particle B, substituting the values,

Therefore, the ratio of radii of A and B is Ra : Rb = 0.955 : 0:917 Approximately, it can be written as 1:1.

d is the correct answer

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