To solve this problem, we can use Newton's second law of motion, which states that the net force on an object is equal to its mass times its acceleration.

Let's denote the acceleration of the masses as "a" and the tension in the string as "T".

For the 5 kg mass:
The force acting on the 5 kg mass is its weight, which can be calculated as:
Force = mass * acceleration due to gravity = 5 kg * 9.8 m/s^2 = 49 N
The net force on the 5 kg mass is equal to the tension in the string (T) minus its weight:
T - 49 N = 5 kg * a ----(equation 1)

For the 8 kg mass:
The force acting on the 8 kg mass is its weight, which can be calculated as:
Force = mass * acceleration due to gravity = 8 kg * 9.8 m/s^2 = 78.4 N
The net force on the 8 kg mass is equal to its weight minus the tension in the string:
78.4 N - T = 8 kg * a ----(equation 2)

Since the masses are connected by a string passing over a pulley, the acceleration of both masses will be the same, denoted as "a".

Now, let's solve the simultaneous equations 1 and 2 to find the values of "a" and "T".

Equation 1: T - 49 N = 5 kg * a
Equation 2: 78.4 N - T = 8 kg * a

Let's solve the equations:

T - 49 N = 5 kg * a ----(equation 1)
78.4 N - T = 8 kg * a ----(equation 2)

Adding equation 1 and equation 2:
T - 49 N + 78.4 N - T = 5 kg * a + 8 kg * a
(78.4 N - 49 N) = (5 kg + 8 kg) * a
29.4 N = 13 kg * a

Dividing both sides by 13 kg:
a = 29.4 N / 13 kg
a ≈ 2.26 m/s^2

Substituting the value of "a" back into equation 1 to solve for T:
T - 49 N = 5 kg * a
T - 49 N = 5 kg * 2.26 m/s^2
T ≈ 49 N + 11.3 N
T ≈ 60.3 N

Therefore, the acceleration of the masses is approximately 2.26 m/s^2, and the tension in the string is approximately 60.3 N.

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