The radius of plant A is half the radius of planet B . If the mass of A is ` M_(A)`, what must be the mass of B so that the value of g on B is half of its value on A ?

Explanation

To solve the problem, we need to find the mass of planet B (denoted as \( M_B \)) given that the radius of planet A (\( R_A \)) is half the radius of planet B (\( R_B \)), and the gravitational acceleration on planet B (\( g_B \)) is half that on planet A (\( g_A \)).

### Step-by-Step Solution:

1. **Write the formula for gravitational acceleration**:
The formula for gravitational acceleration \( g \) at the surface of a planet is given by:
\[
g = \frac{G M}{R^2}
...