Two bodies of masses 50 kg and 100 kg are at a distance 1m apart. The intensity of gravitational field at the mid-point of the line joining them is (in joules)

Options

A. 100G
B. 150G
C. 50G
D. 200G

Answer

To solve the problem of finding the intensity of the gravitational field at the midpoint between two masses of 50 kg and 100 kg that are 1 meter apart, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the masses and distance**: We have two masses, \( m_1 = 50 \, \text{kg} \) and \( m_2 = 100 \, \text{kg} \), separated by a distance \( d = 1 \, \text{m} \).

2. **Determine the midpoint**: The midpoint between the two masses is at a distance of \( 0.5 \, \text{m} \) from each mass.

3. **Calculate the gravitational field intensity due to each mass**:
- The gravitational field intensity \( I \) due to a mass \( m \) at a distance \( r \) is given by the formula:
\[ I = \frac{G \cdot m}{r^2} \]
- For mass \( m_1 = 50 \, \text{kg} \):
\[ I_1 = \frac{G \cdot 50}{(0.5)^2} = \frac{G \cdot 50}{0.25} = 200G \]
- For mass \( m_2 = 100 \, \text{kg} \):
\[ I_2 = \frac{G \cdot 100}{(0.5)^2} = \frac{G \cdot 100}{0.25} = 400G \]

4. **Determine the direction of the gravitational field intensities**:
- The gravitational field intensity \( I_1 \) due to \( m_1 \) points towards \( m_1 \).
- The gravitational field intensity \( I_2 \) due to \( m_2 \) points towards \( m_2 \).

5. **Calculate the net gravitational field intensity at the midpoint**:
- Since \( I_1 \) and \( I_2 \) are in opposite directions, we can find the net gravitational field intensity \( I_{net} \) by subtracting the smaller intensity from the larger intensity:
\[ I_{net} = I_2 - I_1 = 400G - 200G = 200G \]

6. **Conclusion**: The intensity of the gravitational field at the midpoint of the line joining the two masses is:
\[ I_{net} = 200G \, \text{(in joules per kg)} \]