A closed cubical box is completely filled with water and is accelerated horizontally towards right with an acceleration a. The resultant normal force by the water on the top of the box.

Options

A. passes through the centre of top
B. passes through a point to the righ of the centre
C. passes through a point to the left of the centre
D. becomes zero

Answer

To solve the problem of finding the resultant normal force exerted by the water on the top of a closed cubical box that is accelerating horizontally, we can follow these steps:

### Step 1: Understand the Setup
We have a closed cubical box filled with water, and the box is accelerating to the right with an acceleration \( a \). The water inside the box will experience forces due to gravity and the acceleration of the box.

**Hint:** Visualize the box and the water inside it. Consider how the acceleration affects the water's behavior.

### Step 2: Identify the Forces Acting on the Water
1. The weight of the water acts downward, which is equal to \( mg \), where \( m \) is the mass of the water and \( g \) is the acceleration due to gravity.
2. There is a normal force \( N \) exerted by the water on the top of the box.

**Hint:** Remember that the weight of the water acts at the center of mass of the water.

### Step 3: Analyze the Effect of Acceleration
Since the box is accelerating to the right, the water will experience a pseudo force acting to the left (due to the non-inertial frame of reference). This pseudo force will cause the water to exert a pressure that is not uniform across the top of the box.

**Hint:** Consider how the pseudo force affects the pressure distribution in the water.

### Step 4: Determine the Pressure Distribution
As the box accelerates, the water will tend to "lag" behind due to inertia, causing a pressure gradient. The pressure will be higher on the left side of the box and lower on the right side.

**Hint:** Think about how pressure varies in a fluid when it is subjected to an external force.

### Step 5: Resultant Normal Force Calculation
The resultant normal force \( N \) exerted by the water on the top of the box will not be acting directly downward but will have a component to the left due to the pressure gradient. The resultant normal force can be considered to act at a point to the left of the center of the top surface of the box.

**Hint:** Visualize the resultant force and its direction concerning the center of the box.

### Step 6: Conclusion
Therefore, the resultant normal force by the water on the top of the box acts to the left of the center of the box.

**Final Answer:** The resultant normal force by the water on the top of the box passes through a point to the left of the center.

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