Centripetal Force: Speed Change w/ Doubled Radius & Force

[brake4country]

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. ?

 

[BvU]

Do a numerical example...

 

[haruspex]

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.

 

[brake4country]

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!

 

[BvU]

Can you still show your calculation ? It doesn't fit at all.

 

[haruspex]

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.

 

[brake4country]

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.

F_c = 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!