The radius of an object moving in uniform circular motion is doubled. How would

Question

The radius of an object moving in uniform circular motion is doubled. How would the speed of the object have to change for the centripetal acceleration to remain the same? (A) It would increase by a factor of 2. (B) It would increase by a factor of Squareroot 2. (C) It would decrease by a factor of 2. (D) It would decrease by a factor of Squareroot 2. (E) It would not change. A child has a toy tied to the end of a string and whirls the toy at constant speed in a horizontal circular path of radius R. The toy completes each revolution of its motion in a time period T. What is the magnitude of the acceleration of the toy? (A) 2 pi R/T (B) 2 pi R^2/T (C) 4 pi R/T^2 (D) 4 pi^2 R/T^2 (E) 4 pi^2 R^2/T^2

Explanation / Answer

2.

ac = v^2/r

if acceleration remains constant then

v^2/r = constant

(v2/v1)^2 = r2/r1

v2 = v1*sqrt (r2/r1)

v2 = v1*sqrt (2*r/r) = v1*sqrt 2

So it will increase by a factor of sqrt 2

The correct option is B.

3.

ac = v^2/r

v = w*r

ac = w^2*r

w = 2*pi/T

ac = 4*pi^2*r/T^2

Correct option is D.

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