Calculate the value of acceleration due to gravity on moon. Given mass of moon `=7.4xx10^(22)` kg, radius of moon`=1740` km.

Explanation

To calculate the acceleration due to gravity on the Moon, we can use the formula for gravitational acceleration:

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

where:
- \( g \) is the acceleration due to gravity,
- \( G \) is the universal gravitational constant, approximately \( 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \),
- \( M \) is the mass of the Moon,
- \( R \) is the radius of the Moon.

### Step 1: Identify the values
- Mass of the Moon, \( M = 7.4 \times 10^{22} \, \text{kg} \)
- Radius of the Moon, \( R = 1740 \, \text{km} = 1740 \times 10^3 \, \text{m} \)

### Step 2: Convert radius to meters
Since the radius is given in kilometers, we need to convert it to meters:
\[ R = 1740 \, \text{km} = 1740 \times 10^3 \, \text{m} = 1.74 \times 10^6 \, \text{m} \]

### Step 3: Substitute values into the formula
Now we can substitute the values into the formula for \( g \):
\[ g = \frac{(6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2)(7.4 \times 10^{22} \, \text{kg})}{(1.74 \times 10^6 \, \text{m})^2} \]

### Step 4: Calculate the denominator
First, calculate \( R^2 \):
\[ R^2 = (1.74 \times 10^6 \, \text{m})^2 = 3.0276 \times 10^{12} \, \text{m}^2 \]

### Step 5: Calculate the numerator
Now calculate the numerator:
\[ GM = (6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2)(7.4 \times 10^{22} \, \text{kg}) = 4.9388 \times 10^{12} \, \text{N m}^2/\text{kg} \]

### Step 6: Calculate \( g \)
Now substitute the values back into the equation for \( g \):
\[ g = \frac{4.9388 \times 10^{12} \, \text{N m}^2/\text{kg}}{3.0276 \times 10^{12} \, \text{m}^2} \]
\[ g \approx 1.63 \, \text{m/s}^2 \]

### Final Answer
The value of acceleration due to gravity on the Moon is approximately \( 1.63 \, \text{m/s}^2 \).

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