Problem D9:
A small ball of mass m is initially moving in a circle with a constant speed. The radius of
the circle is n_{1}, and its speed is v_{0} as shown in the figure. The string
holding the ball passes through a pipe. Now the string is pulled through the pipe which
shortens the radius of the motion. The string is pulled until the radius is n_{2}.
The motion is still circular, but with a faster speed. How much has the kinetic
energy of the ball increased due to pulling the string? If the increase in kinetic energy
is K.E.(final)-K.E.(initial) = Δ K.E. = n_{3} mv_{0}^{2}/2,
what is n_{3}. Note that n_{1} and n_{2} have the same units of distance, and
n_{3} is unitless.

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