If the mass of the sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following is not correct ?

Options

A. Time period of a simple pendulum on the Earth would decrease
B. Walking on the ground would become more difficult
C. Raindrops will fall faster
D. g' on the Earth will not change

Explanation

To solve the problem, we need to analyze the effects of the changes in the mass of the Sun and the universal gravitational constant (G) on the acceleration due to gravity (g) on Earth and the implications for the given options.

### Step-by-Step Solution:

1. **Understanding the Variables**:
- Let the mass of the Sun be \( M_{sun} \).
- The new mass of the Sun is \( \frac{M_{sun}}{10} \).
- The universal gravitational constant is \( G \), and the new value is \( 10G \).

2. **Acceleration due to Gravity**:
- The formula for the acceleration due to gravity at the surface of the Earth is given by:
\[ g = \frac{GM}{R^2} \]
where \( M \) is the mass of the Earth and \( R \) is the radius of the Earth.

3. **Analyzing the Changes**:
- The mass of the Earth \( M \) remains unchanged, and the radius \( R \) also remains unchanged.
- Therefore, the new acceleration due to gravity \( g' \) can be calculated as:
\[ g' = \frac{10G \cdot M}{R^2} = 10 \cdot \frac{GM}{R^2} = 10g \]
This indicates that the acceleration due to gravity increases by a factor of 10.

4. **Evaluating the Options**:
- **Option 1**: "Time period of a simple pendulum on the earth would decrease."
- The time period \( T \) of a simple pendulum is given by:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
- Since \( g' = 10g \), the new time period \( T' \) will be:
\[ T' = 2\pi \sqrt{\frac{L}{10g}} < T \]
- This option is correct.

- **Option 2**: "Walking on the ground would become more difficult."
- As \( g' \) increases, the weight felt by a person increases, making it more difficult to walk. This option is correct.

- **Option 3**: "Raindrops will fall faster."
- With an increase in \( g' \), raindrops will indeed fall faster due to increased gravitational acceleration. This option is correct.

- **Option 4**: "G' on the earth will not change."
- We calculated that \( g' = 10g \), indicating that the acceleration due to gravity has increased. Therefore, this statement is incorrect.

5. **Conclusion**:
- The option that is not correct is **Option 4**.

### Final Answer:
**Option 4 is not correct.**