Molten-wax of mass m drops on a block of mass, M which is oscillating on a frictionless table. Select the incorrect option.

Options

A. amplitude does not change
B. amplitude increase
C. time period decrease
D. time period increases

Explanation

To solve the problem, we need to analyze the effects of the molten wax of mass \( m \) dropping onto a block of mass \( M \) that is oscillating on a frictionless table. We will evaluate the options given in the question to identify the incorrect statement.

### Step-by-Step Solution:

1. **Understanding the System**:
- We have a block of mass \( M \) oscillating on a frictionless table.
- A molten wax of mass \( m \) is dropped onto this block.

2. **Effect on Mass**:
- When the molten wax drops onto the block, the total mass of the system becomes \( M + m \).

3. **Time Period of the Oscillating System**:
- The time period \( T \) of a mass-spring system is given by the formula:
\[ T = 2\pi \sqrt{\frac{M}{k}} \]
- Here, \( k \) is the spring constant.
- Since the mass of the system increases from \( M \) to \( M + m \), the new time period \( T' \) will be:
\[ T' = 2\pi \sqrt{\frac{M + m}{k}} \]
- Since \( M + m > M \), it follows that \( T' > T \). Therefore, the time period increases.

4. **Effect on Amplitude**:
- The amplitude of oscillation is determined by the initial conditions of the system and does not change simply because additional mass is added. Thus, the amplitude remains constant.

5. **Evaluating the Options**:
- **Option 1**: Amplitude does not change. (This is correct)
- **Option 2**: Amplitude increases. (This is incorrect)
- **Option 3**: Time period decreases. (This is incorrect)
- **Option 4**: Time period increases. (This is correct)

### Conclusion:
The incorrect options are:
- Amplitude increases (Option 2)
- Time period decreases (Option 3)

Thus, the answer to the question is that the incorrect options are Option 2 and Option 3.