Answer
$3.33$ rad/s.
Work Step by Step
The initial moment of inertia of $5*10^{-4}$ increases by $0.02*0.1^2$ to $7*10^{-4}$ when the putty is added. Since angular momentum is conserved, the angular speed decreases to $5/7 *4.7 = 3.33$ rad/s.
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