A solid cylinder wheel of mass `M` and radius `R` is pulled by a force `F` applied to the centre of the wheel at `37^@` to the horizontal. If the wheel is to roll without slipping, what is the maximum value of `|F|` ? The coefficients of static and kinetic friction are `mu_(s)=0.40` and `m_(k)=0.30. (sin37^@=3/5)`

Explanation

To solve the problem of determining the maximum value of the force \( |F| \) that can be applied to a solid cylinder wheel of mass \( M \) and radius \( R \) while ensuring it rolls without slipping, we can follow these steps:

### Step 1: Analyze the Forces
The force \( F \) is applied at an angle of \( 37^\circ \) to the horizontal. We can break this force into its horizontal and vertical components:
- Horizontal component: \( F_x = F \cos(37^\circ) = F \cdot \frac{4}{5} \)
- Vertical component: \( F_y = F \sin(37^\circ) = F \cdot \frac{3}{5} \)

### Step 2: Write the Equations of Motion
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