Centripetal Force: Speed Change w/ Doubled Radius & Force

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When the centripetal force and radius are both doubled, the speed of the object is debated among participants. The equation F = mv²/r is used to analyze the situation, leading to the conclusion that the speed increases by a factor of 2. Some participants initially misinterpret the question, leading to confusion about the correct answer. After recalculating, it is clarified that substituting the values correctly shows the speed increase. Ultimately, the correct answer is that the speed increases by a factor of 2.
brake4country
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Homework Statement


The centripetal force acting on an object is doubled. The radius is also doubled. The speed of the object:

(a) increases by a factor of 4
(b) increases by a factor of 2
(c) decreases by a factor of 2
(d) The change in the object's speed depends on its mass

Homework Equations


F = mv2/r

The Attempt at a Solution


So if I substitute 2's in for F and r in the above equation, my 2's cancel but the correct answer is a. ?
 
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Do a numerical example...
 
brake4country said:
The centripetal force acting on an object is doubled.
So if I substitute 2's in for F and r in the above equation, my 2's cancel but the correct answer is a. ?
Not happy with the wording of the question. Centripetal force does not act. It is the force required to be supplied by forces which do act in order to produce a certain motion.
Anyway, I don't get how the 2's would cancel. (Not that I necessarily agree with the supposed answer.). Please post detailed working.
 
I am sorry; an erroneous math calculation. By substituting 2 for both the force and the radius, I get 4 which is (a). Thank you!
 
Can you still show your calculation ? It doesn't fit at all.
 
brake4country said:
I am sorry; an erroneous math calculation. By substituting 2 for both the force and the radius, I get 4 which is (a). Thank you!
As I hinted, I disagree with that answer. Looks like BvU disagrees with it too.
 
Sorry everyone! That's what happens when you don't read the answer choices correctly! Okay here is the original question: the centripetal force acting on an object is doubled. The radius of the object's motion is also doubled. The speed of the object is:
(A) increases by a factor of
(B) increases by a factor of 2
(C) decreases by a factor of 2
(D) the change in the object's speed depends on its mass.

Fc = mv2/r. If I plug in 2 for F and r, I get 2 = mv2/2 = 4 = mv2. Therefore, the correct answer is (B) increases by a factor of 2! Thanks everyone!
 

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