A point mass m is placed inside a spherical shell of radius R and mass M at a distance `R/2` form the centre of the shell. The gravitational force exerted by the shell on the point mass is

Options

A. `(GMm)/( R^(2))`
B. `(2GMm)/(R^(2))`
C. zero
D. `(4Mm)/(R^(2))`

Explanation

To solve the problem of finding the gravitational force exerted by a spherical shell of mass \( M \) on a point mass \( m \) placed inside it at a distance \( \frac{R}{2} \) from the center, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Setup**:
- We have a spherical shell of radius \( R \) and mass \( M \).
- A point mass \( m \) is located inside the shell at a distance \( \frac{R}{2} \) from the center of the shell.

2. **Gravitational Field Inside a Spherical Shell**:
- According to the shell theorem, the gravitational field inside a uniform spherical shell is zero at any point inside the shell. This means that regardless of where the point mass \( m \) is located inside the shell, it will experience no net gravitational force due to the shell.

3. **Calculate the Gravitational Force**:
- The gravitational force \( F \) experienced by the point mass \( m \) can be calculated using the formula:
\[ F = m \cdot E \]
where \( E \) is the gravitational field strength at the location of the mass \( m \).
- Since we established that the gravitational field \( E \) inside the shell is zero, we have:
\[ E = 0 \]

4. **Final Calculation**:
- Substituting \( E = 0 \) into the force equation gives:
\[ F = m \cdot 0 = 0 \]
- Therefore, the gravitational force exerted by the shell on the point mass \( m \) is \( 0 \).

### Conclusion:
The gravitational force exerted by the shell on the point mass is \( 0 \).