The mass of earth is 80 times that of moon. Their diameters are 12800 km and 3200 km respectively. The value of g on moon will be, if its value on earth is `980cm//s^(2)`

Options

A. `98cm//s^(2)`
B. `196cm//s^(2)`
C. `100cm//s^(2)`
D. `294cm//s^(2)`

Explanation

To find the value of gravitational acceleration (g) on the Moon, we can use the relationship between the gravitational acceleration on the surface of a celestial body, its mass, and its radius. The formula for gravitational acceleration (g) is given by:

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

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

Given:
- Mass of Earth \( (M_e) = 80 \times M_m \) (where \( M_m \) is the mass of the Moon),
- Diameter of Earth = 12800 km, thus radius \( R_e = \frac{12800}{2} = 6400 \) km,
- Diameter of Moon = 3200 km, thus radius \( R_m = \frac{3200}{2} = 1600 \) km,
- \( g_e = 980 \, \text{cm/s}^2 \) (gravitational acceleration on Earth).

### Step-by-step Solution:

1. **Express the ratio of gravitational accelerations:**
\[ \frac{g_m}{g_e} = \frac{M_m}{M_e} \cdot \left(\frac{R_e}{R_m}\right)^2 \]

2. **Substitute the known values:**
- Since \( M_e = 80 \times M_m \), we have:
\[ \frac{g_m}{g_e} = \frac{M_m}{80 \times M_m} \cdot \left(\frac{6400}{1600}\right)^2 \]

3. **Simplify the equation:**
\[ \frac{g_m}{g_e} = \frac{1}{80} \cdot \left(4\right)^2 \]
\[ \frac{g_m}{g_e} = \frac{1}{80} \cdot 16 \]
\[ \frac{g_m}{g_e} = \frac{16}{80} = \frac{1}{5} \]

4. **Calculate \( g_m \):**
\[ g_m = g_e \cdot \frac{1}{5} \]
\[ g_m = 980 \, \text{cm/s}^2 \cdot \frac{1}{5} \]
\[ g_m = 196 \, \text{cm/s}^2 \]

Thus, the value of \( g \) on the Moon is \( 196 \, \text{cm/s}^2 \).