A block of mass `M` is being pulley along horizontal surface .The coefficient of friction the block and the surface is `mu` If another block of mass `M//2` is placed on the block and it is pulled is again pulled on the surface , the coefficient of friction the block and the surface will be

Options

A. `mu`
B. `(3mu)/(2)`
C. `2 mu`
D. `(5mu)/(2)`

Explanation

To solve the problem, we need to analyze the situation step by step.

### Step 1: Understand the system
- We have a block of mass \( M \) on a horizontal surface with a coefficient of friction \( \mu \).
- A second block of mass \( \frac{M}{2} \) is placed on top of the first block.

### Step 2: Determine the forces acting on the blocks
- The weight of the first block is \( W_1 = M \cdot g \) (where \( g \) is the acceleration due to gravity).
- The weight of the second block is \( W_2 = \frac{M}{2} \cdot g \).
- The total weight acting downwards on the first block is the sum of the weights of both blocks:
\[ W_{\text{total}} = W_1 + W_2 = M \cdot g + \frac{M}{2} \cdot g = \frac{3M}{2} \cdot g \]

### Step 3: Calculate the normal force
- The normal force \( N \) acting on the first block from the surface is equal to the total weight acting downwards:
\[ N = W_{\text{total}} = \frac{3M}{2} \cdot g \]

### Step 4: Determine the frictional force
- The frictional force \( F_f \) acting on the first block can be calculated using the coefficient of friction:
\[ F_f = \mu \cdot N = \mu \cdot \left(\frac{3M}{2} \cdot g\right) \]

### Step 5: Analyze the coefficient of friction
- The coefficient of friction \( \mu \) is a property of the surfaces in contact and does not change with the normal force. It is defined as:
\[ \mu = \frac{F_f}{N} \]
- Since \( \mu \) is a property of the surfaces in contact (the block and the surface), it remains unchanged regardless of the additional mass placed on the block.

### Conclusion
- The coefficient of friction between the block and the surface remains \( \mu \), even when the second block is added.

### Final Answer
The coefficient of friction between the block and the surface will remain \( \mu \).

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