A block of mass 70 kg is kept on a rough horizontal surface and coefficient of static friction between block and surface is 0.4 . A man is trying to pull the block by applying a horizontal force .The net contact force exerted by the surface on the block is F , then:

Options

A. F must be 700 N
B. F must be 280 N
C. `700 N le F le 754 N`
D. F maybe greater than 754 N

Answer

To solve the problem, we need to find the net contact force exerted by the surface on the block when a horizontal force is applied. The steps are as follows:

### Step 1: Calculate the weight of the block
The weight (W) of the block can be calculated using the formula:
\[ W = mg \]
Where:
- \( m = 70 \, \text{kg} \) (mass of the block)
- \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity)

Calculating:
\[ W = 70 \, \text{kg} \times 10 \, \text{m/s}^2 = 700 \, \text{N} \]

### Step 2: Determine the normal force (N)
On a rough horizontal surface, the normal force (N) is equal to the weight of the block when there are no vertical forces acting on it other than gravity. Therefore:
\[ N = W = 700 \, \text{N} \]

### Step 3: Calculate the limiting frictional force (F_L)
The limiting frictional force can be calculated using the formula:
\[ F_L = \mu_s N \]
Where:
- \( \mu_s = 0.4 \) (coefficient of static friction)

Calculating:
\[ F_L = 0.4 \times 700 \, \text{N} = 280 \, \text{N} \]

### Step 4: Determine the range of the contact force (F)
The contact force (F) can vary depending on the applied force. The minimum value of the contact force occurs when the frictional force is zero, and the maximum value occurs when the frictional force is at its limiting value.

- **Minimum Contact Force**:
\[ F_{\text{min}} = N = 700 \, \text{N} \]

- **Maximum Contact Force**:
Using the Pythagorean theorem, the maximum contact force when the limiting frictional force is acting is given by:
\[ F_{\text{max}} = \sqrt{N^2 + F_L^2} \]
Calculating:
\[ F_{\text{max}} = \sqrt{(700 \, \text{N})^2 + (280 \, \text{N})^2} \]
\[ F_{\text{max}} = \sqrt{490000 + 78400} \]
\[ F_{\text{max}} = \sqrt{568400} \approx 754 \, \text{N} \]

### Conclusion
The contact force (F) exerted by the surface on the block can range from 700 N to approximately 754 N. Thus, the correct option for the net contact force exerted by the surface on the block is that it lies between these two values.