Let the tension in the string be denoted by \(T\) and the acceleration of the system be \(a\).

For particle A (mass 0.65 kg), applying Newton's second law:

\(0.65g - T = 0.65a\)

For particle B (mass 0.35 kg), applying Newton's second law:

\(T - 0.35g = 0.35a\)

Adding these two equations to eliminate \(T\):

\(0.65g - 0.35g = 0.65a + 0.35a\)

\(0.30g = a\)

Substitute \(a = 0.30g\) back into one of the equations to find \(T\):

\(0.65g - T = 0.65(0.30g)\)

\(T = 0.65g - 0.195g\)

\(T = 0.455g\)

Using \(g = 9.8 \text{ m/s}^2\), \(T = 0.455 \times 9.8 = 4.55 \text{ N}\).

The resultant force exerted on the pulley by the string is twice the tension:

\(2T = 2 \times 4.55 = 9.1 \text{ N}\).