A body is in contact with the vertical front part of the truck. The coefficient of friction between the body and the truck is `mu`. The minimum acceleration with which the truck should travel so that the body does not fall down is

Options

A. `mu//g`
B. `mu g`
C. `g//mu`
D. `mu^(2) g`

Answer

To solve the problem, we need to analyze the forces acting on the body in contact with the vertical front part of the truck. The goal is to find the minimum acceleration of the truck such that the body does not fall down due to gravity.

### Step-by-Step Solution:

1. **Identify the Forces Acting on the Body:**
- The weight of the body acts downward and is given by \( W = mg \), where \( m \) is the mass of the body and \( g \) is the acceleration due to gravity.
- The normal force \( N \) acts perpendicular to the surface of contact (which is vertical in this case).
- The frictional force \( f \) acts upward, opposing the weight of the body. The maximum static frictional force can be expressed as \( f = \mu N \), where \( \mu \) is the coefficient of friction.

2. **Set Up the Equations:**
- For the body to remain in contact with the truck and not fall, the upward frictional force must balance the downward weight of the body. Thus, we have:
\[ f = mg \]
- Substituting the expression for friction, we get:
\[ \mu N = mg \]

3. **Relate Normal Force to Truck's Acceleration:**
- The normal force \( N \) is equal to the net force required to accelerate the body with the truck. If the truck accelerates with an acceleration \( a \), then the net force acting on the body in the horizontal direction is given by:
\[ N = ma \]
- Therefore, we can substitute \( N \) in the friction equation:
\[ \mu (ma) = mg \]

4. **Solve for Truck's Acceleration:**
- Rearranging the equation gives:
\[ a = \frac{g}{\mu} \]

### Final Answer:
The minimum acceleration with which the truck should travel so that the body does not fall down is:
\[ a = \frac{g}{\mu} \]