Question

Object A moves in uniform circular motion. Identical object B experiences an identical force and also moves in uniform circular motion, but is three times farther from the axis of revolution than object A is. Which object is moving at a greater speed?

A. object A
B. object B
C. Neither; they are moving at the same speed.
D. You would need to know the actual masses to figure this out.

Answer 1

D. You would need to know the actual masses to figure this out

Step-by-step explanation:

A body will be in uniform circular motion if a force which is always directed towards the center acts on it.this force is called centripetal force.

for a body of mass m rotating in a circle of radius r with a velocity v centripetal force F is given by,

`F=(mv^(2) )/(r)`

from the question we know,

`3 r_(A)  = r_(B)`

where
`r_(A)  ,r_(B)` are radii of paths of A and B respectively.

since centripetal forces are equal

`F_(A)  = F_(B)`

`(m_(A)v_(A) ^(2)  )/(r_(A) )  =   (m_(B)v_(B) ^(2)  )/(r_(B) )`

from this equation it is clear that ratio of velocities depends on the masses of bodies so we need the actual masses or at least the ratio of masses to to know which travels faster.