A rock is whirled on the end of a string in a horizontal circle of radius R with a constant period T. If the radius of the circle is reduced to R/3, while the period remains T, what happens to the centripetal acceleration of the rock?
A) The centripetal acceleration remains the same.
B) The centripetal acceleration increases by a factor of 3.
C) The centripetal acceleration increases by a factor of 9.
D) The centripetal acceleration decreases by a factor of 3.
E) The centripetal acceleration decreases by a factor of 9.
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C) The centripetal acceleration increases by a factor of 9.
The formula for centripetal acceleration is a = v^2 / r, where v is the velocity and r is the radius. If the radius is reduced to R/3, the denominator of the equation becomes smaller, which means the overall value for acceleration becomes larger. Since the radius is squared in the denominator, the acceleration increases by a factor of 9.
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