Consider the following A and B, and identify the correct choice in the given answers.
A) For a body resting on a rough horizontal table, it is easier to pull at angle that push at the same angle to cause motion
B) A body sliding down a rough inclined plane of inclination equal to angle of friction has nonzero acceleration

Options

A. A and B are true
B. A is true but B is false
C. A is false but B is true
D. A and B are false

Answer

To solve the problem, we need to analyze the two statements A and B separately.

### Step 1: Analyze Statement A
**Statement A:** For a body resting on a rough horizontal table, it is easier to pull at an angle than to push at the same angle to cause motion.

1. **Identify Forces When Pulling:**
- When pulling the body at an angle θ, the applied force \( F \) can be broken down into two components:
- Horizontal component: \( F \cos \theta \)
- Vertical component: \( F \sin \theta \)
- The weight of the body \( mg \) acts downward.
- The normal force \( N \) acts upward and is given by:
\[ N = mg - F \sin \theta \]
- The frictional force \( f \) opposing the motion is:
\[ f = \mu N = \mu (mg - F \sin \theta) \]

2. **Identify Forces When Pushing:**
- When pushing the body at the same angle θ, the components of the applied force are:
- Horizontal component: \( F \cos \theta \)
- Vertical component: \( F \sin \theta \)
- The normal force \( N \) in this case is:
\[ N = mg + F \sin \theta \]
- The frictional force \( f' \) opposing the motion is:
\[ f' = \mu N = \mu (mg + F \sin \theta) \]

3. **Comparison of Frictional Forces:**
- When pulling, the frictional force is:
\[ f = \mu (mg - F \sin \theta) \]
- When pushing, the frictional force is:
\[ f' = \mu (mg + F \sin \theta) \]
- Since \( f < f' \), it is easier to pull the body than to push it.

**Conclusion for Statement A:** True.

### Step 2: Analyze Statement B
**Statement B:** A body sliding down a rough inclined plane of inclination equal to the angle of friction has nonzero acceleration.

1. **Understanding Forces on the Inclined Plane:**
- On an inclined plane with angle θ, the gravitational force can be resolved into two components:
- Parallel to the incline: \( mg \sin \theta \)
- Perpendicular to the incline: \( mg \cos \theta \)

2. **Frictional Force:**
- The maximum static frictional force is given by:
\[ f_{\text{friction}} = \mu N = \mu (mg \cos \theta) \]
- If the angle of inclination θ is equal to the angle of friction, then:
\[ \mu = \tan \theta \]
- Therefore, the frictional force becomes:
\[ f_{\text{friction}} = mg \sin \theta \]

3. **Net Force and Acceleration:**
- When the body is sliding down, the net force acting on it is:
\[ F_{\text{net}} = mg \sin \theta - f_{\text{friction}} = mg \sin \theta - mg \sin \theta = 0 \]
- Since the net force is zero, the acceleration is also zero.

**Conclusion for Statement B:** False.

### Final Answer
- Statement A is true, and Statement B is false.
- Therefore, the correct choice is: **A is true but B is false.**

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