Value of g on the surface of earth is `9.8 m//s^(2)`. Find its value on the surface of a planet whose mass and radius both are two times that of earth.

Explanation

To find the value of \( g \) on the surface of a planet whose mass and radius are both two times that of Earth, we can use the formula for gravitational acceleration:

\[ g = \frac{GM}{R^2} \]

Where:
- \( G \) is the universal gravitational constant,
- \( M \) is the mass of the planet,
- \( R \) is the radius of the planet.

### Step 1: Identify the values for Earth
Let:
- Mass of Earth \( M_e \)
- Radius of Earth \( R_e \)
- Gravitational acceleration on Earth \( g_e = 9.8 \, \text{m/s}^2 \)

### Step 2: Determine the mass and radius of the new planet
Given that the mass and radius of the new planet are both twice that of Earth:
- Mass of the planet \( M = 2M_e \)
- Radius of the planet \( R = 2R_e \)

### Step 3: Substitute values into the formula
Now, substituting the values into the formula for \( g \):

\[ g' = \frac{G(2M_e)}{(2R_e)^2} \]

### Step 4: Simplify the equation
Now simplify the equation:

\[ g' = \frac{2GM_e}{4R_e^2} \]

This can be simplified further:

\[ g' = \frac{1}{2} \cdot \frac{GM_e}{R_e^2} \]

### Step 5: Relate it to Earth's gravitational acceleration
We know that:

\[ g_e = \frac{GM_e}{R_e^2} \]

Thus, we can substitute \( g_e \) into the equation:

\[ g' = \frac{1}{2} g_e \]

### Step 6: Calculate the value of \( g' \)
Now substituting the value of \( g_e \):

\[ g' = \frac{1}{2} \cdot 9.8 \, \text{m/s}^2 = 4.9 \, \text{m/s}^2 \]

### Conclusion
The value of \( g \) on the surface of the planet whose mass and radius are both two times that of Earth is:

\[ g' = 4.9 \, \text{m/s}^2 \]