If the distance between the sun and the earth is increased by four times then the attraction between the two will

Options

A. Remain constant
B. Decrease by 89%
C. Decrease by 91%
D. Decrease by 93.75%

Answer

To solve the problem of how the gravitational attraction between the Sun and the Earth changes when the distance between them is increased by four times, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Gravitational Force Formula**:
The gravitational force \( F \) between two masses \( m_1 \) and \( m_2 \) separated by a distance \( R \) is given by Newton's law of gravitation:
\[ F = \frac{G \cdot m_1 \cdot m_2}{R^2} \]
where \( G \) is the gravitational constant.

2. **Identify the Initial Conditions**:
Let \( F \) be the initial gravitational force when the distance is \( R \):
\[ F = \frac{G \cdot m_1 \cdot m_2}{R^2} \]

3. **Determine the New Distance**:
If the distance is increased by four times, the new distance \( R' \) becomes:
\[ R' = 4R \]

4. **Calculate the New Gravitational Force**:
The new gravitational force \( F' \) at the new distance \( R' \) is:
\[ F' = \frac{G \cdot m_1 \cdot m_2}{(4R)^2} \]
Simplifying this, we have:
\[ F' = \frac{G \cdot m_1 \cdot m_2}{16R^2} \]

5. **Relate the New Force to the Original Force**:
We can express \( F' \) in terms of \( F \):
\[ F' = \frac{F}{16} \]
This means the new gravitational force is \( \frac{1}{16} \) of the original force.

6. **Calculate the Change in Force**:
The change in force can be calculated as:
\[ \text{Change} = F - F' = F - \frac{F}{16} = \frac{16F}{16} - \frac{F}{16} = \frac{15F}{16} \]

7. **Calculate the Percentage Decrease**:
The percentage decrease in the gravitational force is given by:
\[ \text{Percentage Decrease} = \frac{\text{Change}}{F} \times 100 = \frac{\frac{15F}{16}}{F} \times 100 = \frac{15}{16} \times 100 \]
Simplifying this gives:
\[ \text{Percentage Decrease} = 93.75\% \]

### Final Answer:
The gravitational attraction between the Sun and the Earth will decrease by **93.75%** when the distance between them is increased by four times.