If the mass of sun were ten times smaller and gravitational consitant `G` were ten times larger in magnitudes

Options

A. Walking on ground would become more difficult.
B. The acceleration due to gravity on earth will not change.
C. Raindrops will fall much faster.
D. Airplanes will have to travel much faster.

Explanation

To solve the problem, we will analyze the effects of changing the mass of the Sun and the gravitational constant \( G \) on various physical phenomena.

### Given:
- The mass of the Sun is 10 times smaller.
- The gravitational constant \( G \) is 10 times larger.

### Step 1: Understanding the Acceleration due to Gravity
The acceleration due to gravity \( g \) at the surface of the Earth is given by the formula:
\[ g = \frac{G \cdot M_e}{R_e^2} \]
where:
- \( G \) = gravitational constant
- \( M_e \) = mass of the Earth
- \( R_e \) = radius of the Earth

### Step 2: Calculate the New Gravitational Constant
If \( G \) is increased by a factor of 10, we have:
\[ G' = 10G \]

### Step 3: Analyze the Effect on Acceleration due to Gravity
Substituting \( G' \) into the formula for \( g \):
\[ g' = \frac{G' \cdot M_e}{R_e^2} = \frac{10G \cdot M_e}{R_e^2} = 10 \cdot \frac{G \cdot M_e}{R_e^2} = 10g \]
This shows that the new acceleration due to gravity \( g' \) is 10 times the original \( g \).

### Step 4: Analyzing the Statements
1. **Walking on the ground would become more difficult**:
- Since weight \( W = mg \), if \( g \) increases, weight also increases. Thus, walking would indeed become more difficult. **This statement is correct.**

2. **The acceleration due to gravity on Earth will not change**:
- As calculated, \( g' = 10g \), so this statement is incorrect. **This statement is not correct.**

3. **Raindrops will fall much faster**:
- The terminal velocity of raindrops is proportional to \( g \). If \( g \) increases, the terminal velocity will also increase, meaning raindrops will fall faster. **This statement is correct.**

4. **Airplanes will have to travel much faster**:
- With an increase in \( g \), airplanes need to generate more lift to overcome the increased gravitational pull. This means they will need to travel faster. **This statement is correct.**

### Conclusion:
- The correct statements are:
- Walking on the ground would become more difficult.
- Raindrops will fall much faster.
- Airplanes will have to travel much faster.
- The statement that the acceleration due to gravity on Earth will not change is incorrect.