Solution:
After closing the switch:
1. Potential equality: \(\frac{Q_1}{R} = \frac{Q_2}{3R} \Rightarrow Q_2 = 3Q_1\).
2. Charge conservation: \(Q_1 + Q_2 = 36Q \Rightarrow Q_1 + 3Q_1 = 36Q \Rightarrow Q_1 = 9Q\).
Final charge on the smaller sphere = 9Q.
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