Which of the following statements are incorrect?

Options

A. If there were no friction, work needed to be done to move a body up an inclined plane will be zero.
B. If there were no friction, the moving vechicles could not be stopped even by locking the breakes
C. As the angle of inclination is increased, the normal reaction on the body placed on it increases
D. A duster weighing 0.5 N is pressed against a vertical board with a force of 11 N If the coefficient of friction is 0.5 the work done in rubbing it upwards through a distance of 10 cm is 0.55 J

Answer

To determine which statements are incorrect, we will analyze each statement step-by-step.

### Step 1: Analyze the First Statement
**Statement:** If there were no friction, work needed to be done to move a body up an inclined plane will be zero.

**Analysis:**
- When moving a body up an inclined plane, work is done against gravity.
- Even in the absence of friction, the gravitational force acting on the body must be overcome.
- Therefore, work is still required to move the body up the incline.

**Conclusion:** This statement is **incorrect**.

### Step 2: Analyze the Second Statement
**Statement:** If there were no friction, the moving vehicle could not be stopped even by locking the brake.

**Analysis:**
- When brakes are locked, kinetic friction is what helps to stop the vehicle.
- If there is no friction, the vehicle will continue to move at a constant speed due to inertia.
- Thus, without friction, the vehicle cannot be stopped.

**Conclusion:** This statement is **correct**.

### Step 3: Analyze the Third Statement
**Statement:** As the angle of inclination increases, the normal reaction on the body placed on it increases.

**Analysis:**
- The normal force on an inclined plane is given by the formula: \( N = mg \cos(\theta) \).
- As the angle \( \theta \) increases, \( \cos(\theta) \) decreases, leading to a decrease in the normal force.
- Therefore, the normal reaction does not increase with the angle of inclination.

**Conclusion:** This statement is **incorrect**.

### Step 4: Analyze the Fourth Statement
**Statement:** A duster weighing 0.5 N is placed against a vertical board with a force of 11 N. If the coefficient of friction is 0.5, the work done in rubbing it upward through a distance of 10 centimeters is 0.55 Joules.

**Analysis:**
1. Calculate the frictional force:
- Normal force \( N = 11 \, \text{N} \).
- Coefficient of friction \( \mu = 0.5 \).
- Frictional force \( F_f = \mu \cdot N = 0.5 \cdot 11 = 5.5 \, \text{N} \).

2. Convert the distance from centimeters to meters:
- Distance \( d = 10 \, \text{cm} = 0.1 \, \text{m} \).

3. Calculate the work done against friction:
- Work done \( W = F_f \cdot d = 5.5 \, \text{N} \cdot 0.1 \, \text{m} = 0.55 \, \text{J} \).

**Conclusion:** This statement is **correct**.

### Final Conclusion
The incorrect statements are:
- Statement 1: "If there were no friction, work needed to be done to move a body up an inclined plane will be zero."
- Statement 3: "As the angle of inclination increases, the normal reaction on the body placed on it increases."