An object rests on a horizontal frictionless surface. A horizontal force of magnitude F is applied. This force produces an acceleration

Options

A. only if F is larger than the weight of the object
B. only while the object suddenly changes from rest to motion
C. always
D. only if the inertia of the object decreases.

Answer

To solve the problem, we need to determine the acceleration produced by a horizontal force \( F \) applied to an object resting on a horizontal frictionless surface.

### Step-by-Step Solution:

1. **Identify the Forces Acting on the Object:**
- The object has a weight \( mg \) acting downwards due to gravity.
- There is a normal force \( N \) acting upwards, which balances the weight of the object. Since the surface is horizontal and frictionless, \( N = mg \).

2. **Understand the Effect of the Applied Force:**
- A horizontal force \( F \) is applied to the object. This force will cause the object to accelerate horizontally.
- The vertical forces (weight and normal force) do not affect the horizontal motion because they are balanced.

3. **Apply Newton's Second Law:**
- According to Newton's second law, the acceleration \( a \) of an object is given by the formula:
\[ a = \frac{F}{m} \]
- Here, \( F \) is the net force acting on the object, and \( m \) is the mass of the object.

4. **Determine the Acceleration:**
- Since the only horizontal force acting on the object is \( F \), the acceleration produced by this force is:
\[ a = \frac{F}{m} \]
- This means that the acceleration is directly proportional to the applied force and inversely proportional to the mass of the object.

5. **Analyze the Options Given:**
- **Option 1:** "Only if \( F \) is larger than the weight of the object" - Incorrect, as the weight does not affect horizontal acceleration.
- **Option 2:** "Only while the object suddenly changes from rest to motion" - Incorrect, as acceleration occurs regardless of the initial state of motion.
- **Option 3:** "Always" - Correct, as acceleration occurs whenever a force is applied, regardless of the object's initial state.
- **Option 4:** "Only if the inertia of the object decreases" - Incorrect, as inertia is a property of mass and does not change.

6. **Conclusion:**
- The correct answer is **Option 3: Always**. The object will always experience acceleration when a horizontal force is applied, regardless of whether it is at rest or in motion.