A block of weight 100N is lying on a rough horizontal surface. If coefficient of friction `1//sqrt(3)`. The least possible force that can move the block is

Options

A. `100/sqrt(3)`
B. `100sqrt(3)`
C. `50sqrt(3)`
D. `50 N`

Answer

To solve the problem, we need to find the least possible force required to move a block resting on a rough horizontal surface. The weight of the block and the coefficient of friction are given. Let's go through the solution step by step.

### Step 1: Understand the given data
- Weight of the block (W) = 100 N
- Coefficient of friction (μ) = \( \frac{1}{\sqrt{3}} \)

### Step 2: Identify the forces acting on the block
The forces acting on the block include:
- The weight of the block acting downwards (100 N).
- The normal force (N) acting upwards, which is equal to the weight of the block since it is on a horizontal surface.
- The frictional force (f) acting opposite to the direction of the applied force.

### Step 3: Calculate the normal force
Since the block is resting on a horizontal surface and there are no vertical forces acting other than weight and normal force, we have:
\[ N = W = 100 \, \text{N} \]

### Step 4: Calculate the frictional force
The frictional force can be calculated using the formula:
\[ f = \mu \cdot N \]
Substituting the known values:
\[ f = \frac{1}{\sqrt{3}} \cdot 100 \]
\[ f = \frac{100}{\sqrt{3}} \, \text{N} \]

### Step 5: Determine the least force required to move the block
To move the block, the applied force (F) must be greater than or equal to the frictional force. Therefore, the least possible force required to move the block is:
\[ F \geq f \]
\[ F \geq \frac{100}{\sqrt{3}} \, \text{N} \]

### Conclusion
The least possible force that can move the block is:
\[ F = \frac{100}{\sqrt{3}} \, \text{N} \]