The acceleration due to gravity on the surface of the earth is `10 ms^(-2)` . The mass of the planet . Mars as compared to earth is 1/10 and radius is 1/2 . Determine the gravitational acceleration of a body on the surface on Mars .

Answer

To determine the gravitational acceleration on the surface of Mars, we can use the formula for gravitational acceleration:

\[ g = \frac{G \cdot M}{R^2} \]

where:
- \( g \) is the acceleration due to gravity,
- \( G \) is the universal gravitational constant,
- \( M \) is the mass of the planet,
- \( R \) is the radius of the planet.

### Step-by-Step Solution:

1. **Identify the values for Earth**:
- The acceleration due to gravity on Earth (\( g_E \)) is given as \( 10 \, \text{m/s}^2 \).
- Let the mass of Earth be \( M_E \) and the radius of Earth be \( R_E \).

2. **Identify the values for Mars**:
- The mass of Mars (\( M_M \)) compared to Earth is \( \frac{1}{10} M_E \).
- The radius of Mars (\( R_M \)) compared to Earth is \( \frac{1}{2} R_E \).

3. **Substituting Mars' values into the gravitational acceleration formula**:
- The formula for gravitational acceleration on Mars (\( g_M \)) can be expressed as:
\[ g_M = \frac{G \cdot M_M}{R_M^2} \]
- Substituting for \( M_M \) and \( R_M \):
\[ g_M = \frac{G \cdot \left(\frac{1}{10} M_E\right)}{\left(\frac{1}{2} R_E\right)^2} \]

4. **Simplifying the expression**:
- The denominator becomes:
\[ \left(\frac{1}{2} R_E\right)^2 = \frac{1}{4} R_E^2 \]
- Thus, we can rewrite \( g_M \):
\[ g_M = \frac{G \cdot \left(\frac{1}{10} M_E\right)}{\frac{1}{4} R_E^2} = \frac{G \cdot M_E}{R_E^2} \cdot \frac{1}{10} \cdot 4 \]

5. **Using the known value of \( g_E \)**:
- We know that \( g_E = \frac{G \cdot M_E}{R_E^2} = 10 \, \text{m/s}^2 \).
- Therefore, substituting this into the equation gives:
\[ g_M = 10 \cdot \frac{4}{10} = 4 \, \text{m/s}^2 \]

### Final Result:
The gravitational acceleration on the surface of Mars is \( 4 \, \text{m/s}^2 \).