A rectangular wooden box `10 cm xx 20cm xx 40 cm` is size is kept on a horizontal surface with its of lergest are on the surface .A minimum force of `10 N` applied are on the surface sets the box in sliding motion along the surface If the surface, minimum force applied parallel to the surface , to set the box in motion , is

Options

A. less than `10 N`
B. May be greater or less than `10 N`
C. greater than `10 N`
D. equal to `10 N`

Explanation

To solve the problem, we need to determine the minimum force required to set the rectangular wooden box in motion when it is placed on a horizontal surface. The dimensions of the box are given as 10 cm x 20 cm x 40 cm, and we know that a minimum force of 10 N is required to set it in sliding motion.

### Step-by-Step Solution:

1. **Identify the Weight of the Box**:
- The weight (W) of the box can be calculated using the formula:
\[ W = mg \]
- Here, \(m\) is the mass of the box and \(g\) is the acceleration due to gravity (approximately \(9.81 \, \text{m/s}^2\)).

2. **Determine the Normal Force (N)**:
- Since the box is resting on a horizontal surface and not moving vertically, the normal force (N) acting on the box is equal to its weight:
\[ N = W = mg \]

3. **Calculate the Limiting Friction (F_f)**:
- The limiting friction force can be expressed as:
\[ F_f = \mu N \]
- Where \(\mu\) is the coefficient of friction between the box and the surface.

4. **Set Up the Equation for Motion**:
- To set the box in motion, the applied force (F) must be equal to or greater than the limiting friction:
\[ F \geq F_f \]
- Therefore:
\[ F \geq \mu mg \]

5. **Use Given Information**:
- We know that the minimum force required to set the box in motion is 10 N:
\[ 10 \, \text{N} = \mu mg \]

6. **Conclusion**:
- Since the problem states that the minimum force required to set the box in motion remains the same regardless of the contact area (as long as the box is on the same surface), we conclude that the minimum force required to set the box in motion, when applied parallel to the surface, is also:
\[ \text{Minimum Force} = 10 \, \text{N} \]

### Final Answer:
The minimum force required to set the box in motion is **10 N**.