Whathat will be the acceleration due to gravity on a planet whose mass is 4 times that of earth and identical in size ?

Explanation

To find the acceleration due to gravity on a planet whose mass is four times that of Earth and has the same radius, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the formula for acceleration due to gravity (g)**:
The acceleration due to gravity at the surface of a planet is given by the formula:
\[ g = \frac{GM}{R^2} \]
where:
- \( G \) is the universal gravitational constant,
- \( M \) is the mass of the planet,
- \( R \) is the radius of the planet.

2. **Identify the mass and radius of the new planet**:
According to the problem, the mass of the new planet is four times that of Earth. Let:
- Mass of Earth = \( M \)
- Mass of the new planet = \( 4M \)
The radius of the new planet is identical to that of Earth, so:
- Radius of Earth = \( R \)
- Radius of the new planet = \( R \)

3. **Substitute the values into the formula**:
We can now substitute the mass and radius of the new planet into the formula for \( g \):
\[ g' = \frac{G(4M)}{R^2} \]
This simplifies to:
\[ g' = 4 \cdot \frac{GM}{R^2} \]

4. **Relate it to Earth's gravity**:
We know that the acceleration due to gravity on Earth is:
\[ g = \frac{GM}{R^2} \]
Therefore, we can express \( g' \) in terms of \( g \):
\[ g' = 4g \]

5. **Substitute the value of Earth's gravity**:
The acceleration due to gravity on Earth is approximately \( 9.8 \, \text{m/s}^2 \). Thus:
\[ g' = 4 \cdot 9.8 \, \text{m/s}^2 \]

6. **Calculate the final value**:
\[ g' = 39.2 \, \text{m/s}^2 \]

### Final Answer:
The acceleration due to gravity on the planet whose mass is four times that of Earth and has the same radius is \( 39.2 \, \text{m/s}^2 \).

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