Write the net force on the first particle and on the second particle in terms of the unknown tension. Then, note that their accelerations are the same, so note that for both particles, and then solve for the tension.
A particle of mass 0.5kg is suspended from a vertical string. By means of another string, a second particle is suspended from the first of mass 0.4kg. A force of 10N is applied to the upper string and the particle moves upwards. Find the tension in the lower string and the acceleration of the system.
Note: Assume resistances other than those provided, and g, which is to be approximated by 9.8N, are null.
Answer: Tension 4.44N, acceleration 1.31 m/s^2