A particle moves under force `F =5(x -2)^(3)` .Motion of the particle is

Options

A. Translatory
B. Oscillatory
C. SHM
D. All of these

Answer

To determine the type of motion of a particle moving under the force \( F = 5(x - 2)^3 \), we can analyze the force equation and compare it to the standard forms of motion.

### Step-by-Step Solution:

1. **Identify the Force Equation**:
The force acting on the particle is given by:
\[ F = 5(x - 2)^3 \]

2. **Analyze the Form of the Force**:
The force can be expressed in a general form:
\[ F = k(x - a)^n \]
where \( k = 5 \), \( a = 2 \), and \( n = 3 \). Here, \( n \) is an odd number.

3. **Determine the Type of Motion**:
- If \( n \) is odd, the motion can be oscillatory. However, for oscillatory motion, the force should typically be in the form \( F = -kx \) or \( F = -k(x - a) \) which indicates restoring force towards an equilibrium position.
- In our case, the force is \( F = 5(x - 2)^3 \), which is positive when \( x > 2 \) and negative when \( x < 2 \). This means that the force does not act as a restoring force that pulls the particle back towards an equilibrium position.

4. **Conclusion**:
Since the force does not provide a restoring effect and is not in the form required for simple harmonic motion (SHM), we conclude that the motion of the particle is translatory.

Thus, the motion of the particle is **translatory**.

### Final Answer:
The motion of the particle is translatory.

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