The gravitational force between two bodies is `6.67xx10^(-7) N` when the distance between their centres is `10m`. If the mass of first body is `800 kg`, then the mass of second body is

Options

A. `1000 kg`
B. `1250 kg`
C. `1500 kg`
D. `2000 kg`

Explanation

To find the mass of the second body (M2) using the gravitational force formula, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the known values**:
- Gravitational force (F) = \(6.67 \times 10^{-7} \, \text{N}\)
- Mass of the first body (M1) = \(800 \, \text{kg}\)
- Distance between the centers of the two bodies (R) = \(10 \, \text{m}\)
- Universal gravitational constant (G) = \(6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2\)

2. **Write the formula for gravitational force**:
\[ F = \frac{G \cdot M1 \cdot M2}{R^2} \]

3. **Rearrange the formula to solve for M2**:
\[ M2 = \frac{F \cdot R^2}{G \cdot M1} \]

4. **Substitute the known values into the equation**:
- First, calculate \(R^2\):
\[ R^2 = 10^2 = 100 \, \text{m}^2 \]
- Now substitute all values into the rearranged formula:
\[ M2 = \frac{(6.67 \times 10^{-7} \, \text{N}) \cdot (100 \, \text{m}^2)}{(6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2) \cdot (800 \, \text{kg})} \]

5. **Calculate the numerator**:
\[ \text{Numerator} = 6.67 \times 10^{-7} \cdot 100 = 6.67 \times 10^{-5} \]

6. **Calculate the denominator**:
\[ \text{Denominator} = 6.67 \times 10^{-11} \cdot 800 = 5.336 \times 10^{-8} \]

7. **Now calculate M2**:
\[ M2 = \frac{6.67 \times 10^{-5}}{5.336 \times 10^{-8}} \approx 12500 \, \text{kg} \]

8. **Final Answer**:
The mass of the second body (M2) is approximately \(12500 \, \text{kg}\).