Gravitational force acts on a particle due to fixed uniform solid sphere. Neglect other forces. Then particle

Options

A. always moves normal to the radial direction.
B. always moves in the radial direction only.
C. always moves in circular orbit.
D. experiences a force directed along the radial direction only.

Answer

To solve the problem regarding the gravitational force acting on a particle due to a fixed uniform solid sphere, we can analyze the situation step by step.

### Step-by-Step Solution:

1. **Understanding the System**:
- We have a fixed uniform solid sphere and a particle located at some point outside or on the surface of the sphere.
- The gravitational force exerted by the sphere on the particle acts towards the center of the sphere.

2. **Direction of the Gravitational Force**:
- The gravitational force is a central force, which means it always acts along the line joining the center of the sphere and the particle. This line is referred to as the radial direction.

3. **Movement of the Particle**:
- The problem states that we should neglect other forces acting on the particle, so we only consider the gravitational force.
- The particle can move in various ways: it can move in a straight line, in an elliptical path, or in a circular path depending on its initial velocity and position.

4. **Analyzing the Options**:
- **Option 1**: Suggests the particle moves normal to the radial direction. This is incorrect because if the particle were to move in a circular path, it would require a centripetal force directed towards the center, which is provided by the gravitational force. However, the particle can also move in a straight line.
- **Option 2**: States that the particle moves only in the radial direction. This is misleading because while the force is radial, the particle's motion can be in various directions depending on its initial conditions.
- **Option 3**: Claims the particle is moving in a circular orbit. This is not necessarily true as the particle can also move in a straight line or an elliptical path.
- **Option 4**: Correctly states that the particle experiences a force directed along the radial direction only. This is true as the gravitational force acts towards the center of the sphere.

5. **Conclusion**:
- The correct answer is **Option 4**, which states that the particle experiences a force directed along the radial direction only.