A wooden box is placed on a table. The normal force on the box from the table is `N_(1)`. Now another identical box is kept on first box and the normal force on lower block due to upper block is `N_(2)` and normal force on lower block by the table is `N_(3)`. For this situtation, mark out the correct statement (s).

Options

A. `N_(1)=N_(2)=N_(3)`
B. `N_(1) lt N_(2) =N_(3)`
C. `N_(1)=N_(2) lt N_(3)`
D. `N_(1)=N_(2) gt N_(3)`

Explanation

To solve the problem, we need to analyze the forces acting on the wooden boxes placed on the table. Let's break it down step by step.

### Step 1: Analyze the forces on the first box (lower box)
When only one box is placed on the table, the forces acting on it are:
- The gravitational force acting downwards, which is equal to its weight \( mg \).
- The normal force \( N_1 \) acting upwards from the table.

Since the box is in equilibrium (not moving), the normal force must balance the weight of the box. Therefore, we can write the equation:
\[ N_1 = mg \]

### Step 2: Analyze the forces on the second box (upper box)
Now, when a second identical box is placed on top of the first box, we need to consider the forces acting on the upper box:
- The gravitational force acting downwards on the upper box, which is also \( mg \).
- The normal force \( N_2 \) acting upwards from the lower box.

For the upper box to be in equilibrium, the normal force \( N_2 \) must balance the weight of the upper box:
\[ N_2 = mg \]

### Step 3: Analyze the forces on the lower box (combined system)
Now, we consider the forces acting on the lower box due to both boxes:
- The total weight acting downwards is the weight of both boxes, which is \( 2mg \).
- The normal force \( N_3 \) acting upwards from the table.

For the lower box to be in equilibrium, the normal force \( N_3 \) must balance the total weight of both boxes:
\[ N_3 = 2mg \]

### Step 4: Summarize the relationships between the normal forces
From the above analysis, we have:
1. \( N_1 = mg \)
2. \( N_2 = mg \)
3. \( N_3 = 2mg \)

### Conclusion
From the relationships derived:
- \( N_1 \) (normal force from the table on the lower box) is equal to \( mg \).
- \( N_2 \) (normal force from the upper box on the lower box) is also equal to \( mg \).
- \( N_3 \) (normal force from the table on the lower box) is equal to \( 2mg \).

Thus, we can conclude:
\[ N_1 = N_2 < N_3 \]

### Correct Statement
The correct statements regarding the normal forces are:
- \( N_1 = N_2 \)
- \( N_1 < N_3 \)