If the mass of 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 question, we need to analyze the effects of changing the mass of the Sun and the gravitational constant on various physical phenomena. Here’s a step-by-step breakdown:

### Step 1: Understand the Changes
- The mass of the Sun is decreased to one-tenth of its original value.
- The universal gravitational constant (G) is increased to ten times its original value.

### Step 2: Recall the Formula for Acceleration due to Gravity
The acceleration due to gravity (g) on the surface of the Earth is given by the formula:
\[ g = \frac{G \cdot M}{R^2} \]
where:
- \( G \) is the universal gravitational constant,
- \( M \) is the mass of the Earth,
- \( R \) is the radius of the Earth.

### Step 3: Calculate the New Acceleration due to Gravity
With the new values:
- New \( G \) = \( 10G \)
- Mass of Earth \( M \) remains unchanged.
- Radius of Earth \( R \) remains unchanged.

Thus, the new acceleration due to gravity \( g' \) becomes:
\[ g' = \frac{10G \cdot M}{R^2} = 10g \]
This indicates that the acceleration due to gravity has increased tenfold.

### Step 4: Analyze the Options
1. **Time Period of a Simple Pendulum**: The time period \( T \) is given by:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
Since \( g \) has increased, \( T \) will decrease. This statement is correct.

2. **Walking on the Ground**: With increased gravity, it will require more effort to lift feet while walking. This statement is also correct.

3. **Raindrops Falling Faster**: The acceleration due to gravity affects the rate at which raindrops fall. With increased \( g \), raindrops will indeed fall faster. This statement is correct.

4. **g' on Earth will not change**: Since we calculated that \( g' \) has increased to \( 10g \), this statement is incorrect.

### Conclusion
The option that is not correct is that "g' on Earth will not change." Therefore, the answer to the question is that this statement is false.

### Final Answer
The statement that is not correct is: **"g' on Earth will not change."**

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