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 4 times that of Earth and has the same radius as Earth, we can follow these steps:

### Step 1: Understand the formula for acceleration due to gravity
The acceleration due to gravity \( g \) at the surface of a planet 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 planet,
- \( R \) is the radius of the planet.

### Step 2: Define the parameters for Earth and the new planet
Let:
- \( M_e \) be the mass of Earth,
- \( R_e \) be the radius of Earth.

For the new planet:
- The mass \( M_p = 4 \cdot M_e \) (since the mass of the planet is 4 times that of Earth),
- The radius \( R_p = R_e \) (since the planet is identical in size to Earth).

### Step 3: Substitute the values into the formula for the new planet
Using the formula for acceleration due to gravity for the new planet:
\[ g_p = \frac{G \cdot M_p}{R_p^2} \]
Substituting the values we defined:
\[ g_p = \frac{G \cdot (4 \cdot M_e)}{(R_e)^2} \]

### Step 4: Factor out the constants
We can factor out the constants:
\[ g_p = 4 \cdot \frac{G \cdot M_e}{R_e^2} \]
Notice that \( \frac{G \cdot M_e}{R_e^2} \) is the acceleration due to gravity on Earth, denoted as \( g_e \):
\[ g_e = \frac{G \cdot M_e}{R_e^2} \]

### Step 5: Relate the acceleration due to gravity on the new planet to that on Earth
Thus, we can express \( g_p \) in terms of \( g_e \):
\[ g_p = 4 \cdot g_e \]

### Final Answer
The acceleration due to gravity on the planet is \( 4g_e \), where \( g_e \) is the acceleration due to gravity on Earth.