Let the tension in the string be T and the acceleration of the system be a. For particle Q (mass 0.4 kg), applying Newton's second law gives:

\(0.4g - T = 0.4a\)

For particle P (mass 0.6 kg), applying Newton's second law gives:

\(T = 0.6a\)

Adding these two equations to eliminate T gives:

\(0.4g = (0.4 + 0.6)a\)

Solving for a:

\(a = \frac{0.4g}{1} = 4 \text{ m/s}^2\)

Substituting back to find T:

\(T = 0.6a = 0.6 \times 4 = 2.4 \text{ N}\)