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.

in simple terms, the principle states that the buoyancy force on an object is equal to the weight of the fluid displaced by the object, or the density of the fluid multiplied by the submerged volume times the gravitational acceleration, g. this is also known as upthrust.

the first american roller coaster was the mauch chunk switchback railway, built in the mountains of pennsylvania in the mid-1800s. the track, originally built to send coal to a railway, was reconfigured as a "scenic tour."