The tension in the string connected between the blocks is? (The surface is smooth)

1. 80/3 N
2. 40/3 N
3. 50/7 N
4. 26 N

To determine the tension in the string connected between the blocks, we can use Newton's second law of motion. Since the surface is smooth, there is no friction to consider.

Let's denote the two blocks as Block A and Block B. Block A has a mass of 4 kg, and Block B has a mass of 5 kg.

First, let's calculate the gravitational force acting on each block:

Gravitational force on Block A (F_A) = mass of Block A × gravitational acceleration (g)
F_A = 4 kg × 9.81 m/s² = 39.24 N

Gravitational force on Block B (F_B) = mass of Block B × gravitational acceleration (g)
F_B = 5 kg × 9.81 m/s² = 49.05 N

Now, we need to consider the net force acting on the system of these two blocks. Since they are connected by a string and move together, we can treat them as a single system.

Let T be the tension in the string.

Using Newton's second law (F = ma) for the system of blocks:

F_net = (mass of the system) × (acceleration of the system)

The net force is the difference in gravitational forces since there is no horizontal external force:

F_net = F_B - F_A
F_net = 49.05 N - 39.24 N
F_net = 9.81 N

Now, we can find the acceleration (a) of the system using Newton's second law:

F_net = (mass of the system) × a

a = F_net / (mass of the system)
a = 9.81 N / (4 kg + 5 kg)
a = 9.81 N / 9 kg
a = 1.09 m/s²

Now that we have found the acceleration, we can calculate the tension in the string (T) using Block B:

F_net = (mass of Block B) × a

T - F_B = 5 kg × 1.09 m/s²
T = 5.45 N + 49.05 N
T = 54.5 N

So, the tension in the string connected between the blocks is 54.5 N.

None of the provided options match the correct answer of 54.5 N.