Two particles `p` and `q` located at distances `r_p` and `r_q` respectively from the centre of a rotating disc such that `r_p gt r_q`.

Options

A. Both P and Q have the same acceleration
B. BothP and Q do not have any acceleration
C. P has greater acceleration than Q
D. Q has greater acceleration than P

Explanation

To solve the problem, we need to analyze the motion of two particles \( p \) and \( q \) located at distances \( r_p \) and \( r_q \) from the center of a rotating disc, where \( r_p > r_q \).

### Step-by-Step Solution:

1. **Understand the Concept of Acceleration in Circular Motion**:
- In circular motion, the centripetal acceleration \( a \) of an object is given by the formula:
\[ a = \omega^2 r \]
where \( \omega \) is the angular velocity and \( r \) is the radius (or distance from the center).

2. **Identify the Variables**:
- For particle \( p \):
- Distance from the center: \( r_p \)
- Acceleration: \( a_p = \omega^2 r_p \)
- For particle \( q \):
- Distance from the center: \( r_q \)
- Acceleration: \( a_q = \omega^2 r_q \)

3. **Compare the Accelerations**:
- Since both particles are on the same rotating disc, they share the same angular velocity \( \omega \).
- Given that \( r_p > r_q \), we can substitute into the acceleration formulas:
\[ a_p = \omega^2 r_p \quad \text{and} \quad a_q = \omega^2 r_q \]
- Now, since \( r_p > r_q \), it follows that:
\[ a_p > a_q \]

4. **Conclusion**:
- Therefore, particle \( p \) has greater acceleration than particle \( q \).

### Final Answer:
The correct option is that particle \( p \) has greater acceleration than particle \( q \).