Problem Statement:
A pulley fixed to the ceiling of an elevator car carries a thread whose ends are attached to the loads of masses 3m and m. The car starts going up with acceleration g/5. Assuming the masses of the pulley and the thread as well as the pulley on the ceiling car.

Solution:

1. Analysis:
In this problem, we have an elevator car with a pulley fixed to its ceiling. There are two loads attached to the pulley using a thread. The masses of the loads are 3m and m, where m is a constant. The elevator car starts moving upward with an acceleration of g/5, where g is the acceleration due to gravity. We need to determine the masses of the pulley and the thread, as well as the pulley on the ceiling of the car.

2. Free-Body Diagram:
To analyze the forces acting on the system, we draw a free-body diagram. The following forces are present in the system:
- Tension force in the thread on the pulley (T)
- Tension force in the thread on the load of mass 3m (T1)
- Tension force in the thread on the load of mass m (T2)
- Weight of the load of mass 3m (3mg)
- Weight of the load of mass m (mg)
- Normal force exerted by the floor of the elevator car on the loads (N)
- Normal force exerted by the floor of the elevator car on the pulley (N')

3. Equations of Motion:
We can write the equations of motion for the two loads as follows:
- For the load of mass 3m: T1 - 3mg = (3m)(g/5)
- For the load of mass m: T2 - mg = (m)(g/5)

4. Tension in the Thread:
From the equations of motion, we can solve for the tensions in the thread:
- T1 = (3m)(g/5) + 3mg
- T2 = (m)(g/5) + mg

5. Mass of the Pulley:
To determine the mass of the pulley, we need to consider the forces acting on it. The tension in the thread exerts a force on the pulley, and the normal force exerted by the floor of the elevator car counteracts this force. Since the pulley is fixed to the ceiling, it does not accelerate. Therefore, the net force acting on it is zero. We can write the equation as follows:
- T + T' = 0
- T = -T'

6. Mass of the Thread:
Since the thread is assumed to be massless, its mass can be considered negligible.

7. Mass of the Pulley on the Ceiling:
We assume the mass of the pulley on the ceiling is also negligible.

Conclusion:
In this problem, we analyzed the forces acting on the system consisting of an elevator car, a pulley, and two loads. We determined the tensions in the thread and found that the mass of the pulley is negligible. We also assumed the mass of the thread and the pulley on the ceiling to be negligible.