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. `(GMM)/(R^(2))`

Explanation

To solve the problem, we need to determine the gravitational force exerted by a spherical shell of mass \( M \) on a point mass \( m \) located inside the shell at a distance \( \frac{R}{2} \) from the center of the shell.

### Step-by-Step Solution:

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

2. **Gravitational Field Inside a Shell**:
- According to the shell theorem, the gravitational field inside a uniform spherical shell is zero at all points inside the shell. This means that any point inside the shell experiences no net gravitational force due to the mass of the shell.

3. **Calculating the Gravitational Force**:
- The gravitational force \( F \) on the point mass \( m \) can be calculated using the formula:
\[ F = m \cdot g \]
where \( g \) is the gravitational field strength at the location of the mass \( m \).

4. **Substituting the Value of Gravitational Field**:
- Since the gravitational field \( g \) inside the shell is zero, we have:
\[ g = 0 \]
- Therefore, substituting this value into the force equation gives:
\[ F = m \cdot 0 = 0 \]

5. **Conclusion**:
- The gravitational force exerted by the shell on the point mass \( m \) is zero.

### Final Answer:
The gravitational force exerted by the shell on the point mass is \( \mathbf{0} \).

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