Which of the following statements is correct?

Options

A. Torque is the rotational analogue of force.
B. Rolling motion of cylinder down an inclined plane is combination of translation and rotational motion.
C. If the effort arm is larger than the load arm, the mechanical advantage is lesser than one.
D. For the extended body, the centre of mass and centre of gravity do not coincide.

Explanation

To determine which of the statements is correct, let's analyze each statement step-by-step:

### Step 1: Analyze the First Statement
**Statement:** Torque is a rotational analog of force.

**Explanation:**
- In linear motion, force (F) is defined as F = mass (m) × acceleration (a).
- In rotational motion, torque (τ) is defined as τ = moment of inertia (I) × angular acceleration (α).
- The relationship shows that torque plays a similar role in rotational motion as force does in linear motion. Thus, this statement is correct.

### Step 2: Analyze the Second Statement
**Statement:** Rolling motion of a cylinder down an inclined plane is a combination of translation and rotational motion.

**Explanation:**
- When a cylinder rolls down an incline, it undergoes both translational motion (the center of mass moves down the incline) and rotational motion (the cylinder rotates about its axis).
- The relationship between linear velocity (v) and angular velocity (ω) is given by v = rω, where r is the radius of the cylinder.
- This confirms that the cylinder indeed exhibits both types of motion. Thus, this statement is also correct.

### Step 3: Analyze the Third Statement
**Statement:** If the effort arm is larger than the load arm, the mechanical advantage is lesser than one.

**Explanation:**
- Mechanical advantage (MA) is defined as the ratio of output force (load) to input force (effort).
- If the effort arm (R) is larger than the load arm (r), then the output force is greater than the input force, leading to MA > 1.
- Therefore, this statement is incorrect.

### Step 4: Analyze the Fourth Statement
**Statement:** For an extended body, the center of mass and center of gravity do not coincide.

**Explanation:**
- The center of mass is the point where the mass of a body is concentrated, while the center of gravity is the point where the weight of the body acts.
- In a uniform gravitational field, for point masses, the center of mass and center of gravity coincide. However, for extended bodies in non-uniform fields, they may not coincide.
- Thus, this statement is correct.

### Conclusion
The correct statements are:
1. Torque is a rotational analog of force (Correct).
2. Rolling motion of a cylinder down an inclined plane is a combination of translation and rotational motion (Correct).
3. If the effort arm is larger than the load arm, the mechanical advantage is lesser than one (Incorrect).
4. For an extended body, the center of mass and center of gravity do not coincide (Correct).

**Final Answer:** The correct statements are 1, 2, and 4.