The mass of moon 1% of mass of earth. The ratio of gravitational pull of earth on moon and that of moon on earth will be

Options

A. `1:1`
B. `1:10`
C. `1:100`
D. `2:1`

Explanation

To solve the problem of finding the ratio of the gravitational pull of the Earth on the Moon and that of the Moon on the Earth, we can follow these steps:

### Step 1: Define the Masses
Let the mass of the Earth be \( M_E \) and the mass of the Moon be \( M_M \). According to the problem, the mass of the Moon is 1% of the mass of the Earth:
\[ M_M = \frac{1}{100} M_E \]

### Step 2: Write the Formula for Gravitational Force
The formula for the gravitational force \( F \) between two masses is given by:
\[ F = \frac{G M_1 M_2}{R^2} \]
where \( G \) is the gravitational constant, \( M_1 \) and \( M_2 \) are the masses, and \( R \) is the distance between the centers of the two masses.

### Step 3: Calculate the Gravitational Force of the Earth on the Moon
Using the formula, the gravitational force exerted by the Earth on the Moon is:
\[ F_{E \text{ on } M} = \frac{G M_E M_M}{R^2} \]
Substituting \( M_M = \frac{1}{100} M_E \):
\[ F_{E \text{ on } M} = \frac{G M_E \left(\frac{1}{100} M_E\right)}{R^2} = \frac{G M_E^2}{100 R^2} \]

### Step 4: Calculate the Gravitational Force of the Moon on the Earth
Now, the gravitational force exerted by the Moon on the Earth is:
\[ F_{M \text{ on } E} = \frac{G M_M M_E}{R^2} \]
Substituting \( M_M = \frac{1}{100} M_E \):
\[ F_{M \text{ on } E} = \frac{G \left(\frac{1}{100} M_E\right) M_E}{R^2} = \frac{G M_E^2}{100 R^2} \]

### Step 5: Find the Ratio of the Forces
Now, we can find the ratio of the gravitational force of the Earth on the Moon to the gravitational force of the Moon on the Earth:
\[ \text{Ratio} = \frac{F_{E \text{ on } M}}{F_{M \text{ on } E}} = \frac{\frac{G M_E^2}{100 R^2}}{\frac{G M_E^2}{100 R^2}} = 1 \]

### Conclusion
The ratio of the gravitational pull of the Earth on the Moon and that of the Moon on the Earth is:
\[ \text{Ratio} = 1 : 1 \]