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 value of acceleration due to gravity on the Moon, we can use the formula:

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

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, and
- \( R \) is the radius of the Moon.

### Step 1: Identify the given values
- Mass of the Moon, \( M = 7.4 \times 10^{22} \, \text{kg} \)
- Radius of the Moon, \( R = 1740 \, \text{km} = 1740 \times 10^3 \, \text{m} = 1.74 \times 10^6 \, \text{m} \)

### Step 2: Substitute the values into the formula
Using the formula for \( g \):

\[ g = \frac{(6.67 \times 10^{-11}) \times (7.4 \times 10^{22})}{(1.74 \times 10^6)^2} \]

### Step 3: Calculate the denominator
First, calculate \( (1.74 \times 10^6)^2 \):

\[ (1.74 \times 10^6)^2 = 1.74^2 \times (10^6)^2 = 3.0276 \times 10^{12} \, \text{m}^2 \]

### Step 4: Calculate the numerator
Now, calculate the numerator:

\[ 6.67 \times 10^{-11} \times 7.4 \times 10^{22} = 49.378 \times 10^{11} \, \text{N m}^2/\text{kg} \]

### Step 5: Combine the results
Now substitute the numerator and denominator back into the formula for \( g \):

\[ g = \frac{49.378 \times 10^{11}}{3.0276 \times 10^{12}} \]

### Step 6: Simplify the expression
This can be simplified as:

\[ g = \frac{49.378}{3.0276} \times 10^{11 - 12} = \frac{49.378}{3.0276} \times 10^{-1} \]

Calculating \( \frac{49.378}{3.0276} \):

\[ \frac{49.378}{3.0276} \approx 16.32 \]

Thus,

\[ g \approx 16.32 \times 10^{-1} \approx 1.632 \, \text{m/s}^2 \]

### Final Result
The acceleration due to gravity on the Moon is approximately:

\[ g \approx 1.63 \, \text{m/s}^2 \]

---