Assertion:The couple acting on a body is not equal to the rotational KE of the body
Reason: Couple and KE have different dimensions

Options

A. both Assertion and Reason are both are both wrong
B. Assertion is right, Reason is wrong
C. both Assertion and Reason are correct and Reason explains Assertion
D. both Assertion and Reason are correct, but Reason does not explain Assertion

Answer

To solve the question, we need to analyze the assertion and the reason provided:

**Assertion:** The couple acting on a body is not equal to the rotational KE of the body.
**Reason:** Couple and KE have different dimensions.

### Step-by-Step Solution:

1. **Understanding the Concepts:**
- A **couple** consists of two equal and opposite forces acting on a body, which creates a rotational effect. The torque (τ) produced by a couple is given by the product of one of the forces (F) and the distance (d) between the forces:
\[ τ = F \cdot d \]
- **Rotational Kinetic Energy (KE)** is the energy possessed by a rotating body due to its rotation. It is given by the formula:
\[ KE_{rotational} = \frac{1}{2} I \omega^2 \]
where \( I \) is the moment of inertia and \( \omega \) is the angular velocity.

2. **Analyzing the Assertion:**
- The assertion states that the couple acting on a body is not equal to the rotational kinetic energy of the body. This is true because a couple produces torque, which causes rotation, but it does not directly equate to the energy of that rotation. The couple can do work, which then converts to rotational kinetic energy, but they are not the same quantity.

3. **Analyzing the Reason:**
- The reason states that a couple and kinetic energy have different dimensions. This is also true. The dimensions of torque (couple) are \( [M^1 L^2 T^{-2}] \) (force times distance), while the dimensions of energy (kinetic energy) are \( [M^1 L^2 T^{-2}] \). Although they have the same dimensions, the assertion is still valid because it is not about dimensions but about the nature of the quantities.

4. **Conclusion:**
- Since the assertion is true (the couple is not equal to the rotational KE) and the reason is misleading (the dimensions do not affect the equality), we conclude that the assertion is correct, but the reason is not a valid justification for the assertion.

### Final Answer:
Both the assertion and the reason are not valid in the context of their relationship. The assertion is true, but the reason is misleading. Thus, the correct option is that the assertion is true, but the reason is false.