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

Answer

To solve the question, we need to analyze the impact of changes in the mass of the sun and the universal gravitational constant on various physical phenomena.

### Step-by-Step Solution:

1. **Understanding the Changes**:
- The mass of the sun is reduced to 1/10th of its original value.
- The universal gravitational constant \( G \) is increased to 10 times its original value.

2. **Effect on Gravitational Force**:
- The gravitational force \( F \) between two masses is given by Newton's law of gravitation:
\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]
- Here, \( m_1 \) could be the mass of the Earth, \( m_2 \) is the mass of the sun, and \( r \) is the distance between their centers.
- If \( m_2 \) (mass of the sun) is reduced to \( \frac{M}{10} \) and \( G \) is increased to \( 10G \), the new force becomes:
\[ F' = \frac{10G \cdot m_1 \cdot \frac{m_2}{10}}{r^2} = \frac{G \cdot m_1 \cdot m_2}{r^2} = F \]
- Thus, the gravitational force remains unchanged.

3. **Acceleration due to Gravity**:
- The acceleration due to gravity \( g \) at the surface of the Earth is given by:
\[ g = \frac{G \cdot M}{r^2} \]
- With the changes, we have:
\[ g' = \frac{10G \cdot \frac{M}{10}}{r^2} = \frac{G \cdot M}{r^2} = g \]
- Therefore, the acceleration due to gravity on Earth remains unchanged.

4. **Time Period of a Simple Pendulum**:
- The time period \( T \) of a simple pendulum is given by:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
- Since \( g \) remains unchanged, the time period \( T \) will also remain unchanged.

5. **Walking on the Ground**:
- If \( g \) remains unchanged, the difficulty of walking does not increase. So, this statement is incorrect.

6. **Speed of Raindrops**:
- Since \( g \) remains unchanged, the speed of raindrops falling will also not change significantly.

### Conclusion:
- The statement that is **not correct** is: "Gravity on the earth will not change." This is because the gravitational force and acceleration due to gravity remain unchanged.

### Final Answer:
The incorrect statement is: **Gravity on the earth will not change.**