A block of mass M is held against a rough vertical wall by pressing it with a finger . If the coefficient of friction between the block and the wall is `mu` and the acceleration due to gravity is g , calculate the minimum force required to be applied by the finger to hold the block against the wall.

Options

A. `muMg`
B. Mg
C. `(Mg)/(mu)`
D. `2muMg`

Explanation

To solve the problem of finding the minimum force required to hold a block of mass \( M \) against a rough vertical wall, we can follow these steps:

### Step 1: Identify the forces acting on the block
- The block experiences several forces:
- The weight of the block \( W = Mg \) acting downwards (where \( g \) is the acceleration due to gravity).
- A normal force \( N \) acting horizontally from the wall on the block.
- A frictional force \( f \) acting upwards, which opposes the weight of the block.

### Step 2: Understand the role of friction
- The frictional force \( f \) can be expressed in terms of the normal force \( N \) and the coefficient of friction \( \mu \):
\[ f = \mu N \]
- Since the block is not moving, the frictional force must balance the weight of the block:
\[ f = Mg \]

### Step 3: Set up the equation
- From the previous step, we can equate the frictional force to the weight of the block:
\[ \mu N = Mg \]

### Step 4: Solve for the normal force \( N \)
- Rearranging the equation gives us:
\[ N = \frac{Mg}{\mu} \]

### Step 5: Relate the normal force to the force applied by the finger
- The force \( F \) applied by the finger is equal to the normal force \( N \) exerted by the wall on the block:
\[ F = N \]
- Therefore, substituting for \( N \):
\[ F = \frac{Mg}{\mu} \]

### Final Answer
The minimum force required to be applied by the finger to hold the block against the wall is:
\[ F = \frac{Mg}{\mu} \]