1. Understanding the Setup

* Pulley: The pulley is frictionless and weightless, meaning it doesn't resist motion and doesn't contribute to the forces in the system.

* Masses: You have two masses, one of 200g (0.2 kg) and the other of 300g (0.3 kg).

* Cord: The cord is assumed to be inextensible (doesn't stretch) and massless.

2. Forces Involved

* Gravity: The only force acting on the masses is gravity. The heavier mass (300g) experiences a stronger downward force, causing the system to accelerate.

* Tension: The cord exerts an upward tension force on both masses, equal in magnitude but opposite in direction.

3. Finding the Acceleration

* Net force on the system: The net force causing the acceleration is the difference in the gravitational forces on the two masses.

* F_net = (0.3 kg * 9.8 m/s²) - (0.2 kg * 9.8 m/s²) = 0.98 N

* Acceleration: Using Newton's second law (F = ma), we can find the acceleration of the system:

* a = F_net / (total mass) = 0.98 N / (0.3 kg + 0.2 kg) = 1.96 m/s²

4. Motion during the 5th Second

Since the masses are accelerating uniformly, we can use the equations of motion to find the distance traveled during the 5th second.

* First, find the distance traveled in the first 4 seconds:

* d = ut + (1/2)at² (where u = initial velocity = 0)

* d = (1/2) * 1.96 m/s² * (4 s)² = 15.68 m

* Then, find the distance traveled in the first 5 seconds:

* d = (1/2) * 1.96 m/s² * (5 s)² = 24.5 m

* The distance traveled during the 5th second is the difference between these two:

* Distance in 5th second = 24.5 m - 15.68 m = 8.82 m

Therefore, the distance the masses will move during the 5th second after they start is 8.82 meters.