Correct Answer - `(4)/(5) m`
Potential of bigger sphere is `V = (kQ)/b`
When small ball comes in contact with bigger, their potentials will become same. So
`(k q)/a = (k (Q - q))/b`
Neglecting q in comparision to Q, we get
`q = (Q a)/b = 1 mu C`
Apply conservation of energy after collision
`(1)/(2) m (sqrt(2 g h))^2 + ( k qQ)/b = mg h_1 + ( kq Q)/(b + h_1)`
or `h = (4)/(5) m`.