A particle of mass `20 g` experiences a gravitational force of `4.0 N` along positive x - direction. Find the gravitational field at that point.

Explanation

To solve the problem, we need to find the gravitational field at a point where a particle of mass 20 g experiences a gravitational force of 4.0 N. We can use the relationship between gravitational field (E), gravitational force (F), and mass (m).

### Step-by-Step Solution:

1. **Convert the mass from grams to kilograms**:
- The mass of the particle is given as 20 g.
- To convert grams to kilograms, we use the conversion factor \(1 \text{ g} = 0.001 \text{ kg}\).
- Therefore, \( m = 20 \text{ g} = 20 \times 10^{-3} \text{ kg} = 0.020 \text{ kg} \).

2. **Use the formula for gravitational field**:
- The gravitational field (E) is defined as the force (F) experienced by a mass (m) per unit mass.
- The formula is given by:
\[ E = \frac{F}{m} \]
- Here, \( F = 4.0 \text{ N} \) and \( m = 0.020 \text{ kg} \).

3. **Substitute the values into the formula**:
- Now, substituting the values into the formula:
\[ E = \frac{4.0 \text{ N}}{0.020 \text{ kg}} \]

4. **Calculate the gravitational field**:
- Performing the division:
\[ E = \frac{4.0}{0.020} = 200 \text{ N/kg} \]

5. **Determine the direction of the gravitational field**:
- The problem states that the gravitational force acts along the positive x-direction.
- Therefore, the gravitational field vector can be represented as:
\[ \vec{E} = 200 \hat{i} \text{ N/kg} \]

### Final Answer:
The gravitational field at that point is \( \vec{E} = 200 \hat{i} \text{ N/kg} \).

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