Calculate the force of gravitation due to earth on a ball of 1 kg mass lying on the ground.(Mass of earth `=6xx10^(24) kg ` Radius of earth `=6.4xx10^(3)`km and `G=6.7xx10^(-11)Nm^(2)/Kg^(2)`

Options

A. `4.9 N`
B. `9.8 N`
C. `19.2 N`
D. None of the above

Explanation

To calculate the force of gravitation due to Earth on a ball of mass 1 kg lying on the ground, we will use Newton's law of gravitation. The formula for the gravitational force \( F \) between two masses is given by:

\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]

where:
- \( G \) is the gravitational constant, \( 6.7 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \)
- \( m_1 \) is the mass of the first object (the ball), \( 1 \, \text{kg} \)
- \( m_2 \) is the mass of the second object (the Earth), \( 6 \times 10^{24} \, \text{kg} \)
- \( r \) is the distance between the centers of the two masses, which is equal to the radius of the Earth, \( 6.4 \times 10^3 \, \text{km} \) (converted to meters: \( 6.4 \times 10^6 \, \text{m} \))

### Step-by-Step Solution:

1. **Convert the radius of the Earth from kilometers to meters**:
\[ r = 6.4 \times 10^3 \, \text{km} = 6.4 \times 10^3 \times 1000 \, \text{m} = 6.4 \times 10^6 \, \text{m} \]

2. **Substitute the values into the gravitational force formula**:
\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]
Substituting the known values:
\[ F = \frac{(6.7 \times 10^{-11} \, \text{N m}^2/\text{kg}^2) \cdot (1 \, \text{kg}) \cdot (6 \times 10^{24} \, \text{kg})}{(6.4 \times 10^6 \, \text{m})^2} \]

3. **Calculate the denominator \( r^2 \)**:
\[ r^2 = (6.4 \times 10^6 \, \text{m})^2 = 40.96 \times 10^{12} \, \text{m}^2 = 4.096 \times 10^{13} \, \text{m}^2 \]

4. **Calculate the numerator**:
\[ G \cdot m_1 \cdot m_2 = (6.7 \times 10^{-11}) \cdot (1) \cdot (6 \times 10^{24}) = 40.2 \times 10^{13} \, \text{N m}^2/\text{kg} \]

5. **Combine the results to find \( F \)**:
\[ F = \frac{40.2 \times 10^{13}}{4.096 \times 10^{13}} \, \text{N} \]
Simplifying this gives:
\[ F \approx 9.81 \, \text{N} \]

### Final Answer:
The force of gravitation due to Earth on a ball of 1 kg mass lying on the ground is approximately \( 9.81 \, \text{N} \).