Problem Analysis:

To solve this problem, we will first analyze the forces acting on the block and then apply Newton's second law to find the tension in the string connected to the block.

Forces Acting on the Block:

1. Weight: The weight of the block, which is the force due to gravity acting vertically downward. Its magnitude can be calculated using the formula: weight = mass * acceleration due to gravity.
2. Normal Force: The normal force exerted by the flat car on the block, which acts perpendicular to the surface of the flat car. Its magnitude is equal to the weight of the block since the block is not accelerating vertically.
3. Frictional Force: The frictional force between the block and the flat car, which opposes the motion of the block. Its magnitude can be calculated using the formula: frictional force = coefficient of friction * normal force.

Applying Newton's Second Law:

Since the block is connected to the flat car by a light inextensible string, the acceleration of the block is equal to the acceleration of the flat car. Thus, we can apply Newton's second law to the block to find the tension in the string.

The net force acting on the block in the horizontal direction is given by the difference between the tension in the string and the frictional force:

net force = tension - frictional force.

Using Newton's second law (F = ma), we have:

tension - frictional force = mass * acceleration.

Calculation:

Given:
- Acceleration of the flat car (a) = 2 m/s^2.
- Mass of the block (m) = 50 kg.
- Coefficient of friction (μ) = 0.3.

First, we calculate the weight of the block:

weight = mass * acceleration due to gravity = 50 kg * 9.8 m/s^2 = 490 N.

Next, we calculate the normal force:

normal force = weight = 490 N.

Then, we calculate the frictional force:

frictional force = coefficient of friction * normal force = 0.3 * 490 N = 147 N.

Now, we can apply Newton's second law to find the tension in the string:

tension - frictional force = mass * acceleration.

tension - 147 N = 50 kg * 2 m/s^2.

tension - 147 N = 100 N.

tension = 100 N + 147 N = 247 N.

Answer:

The tension in the light inextensible string connected to the block of mass 50 kg is 247 N.