Which of following statements are correct ? l (a) Centre of mass of a body always coincides with the centre of gravity of the body
(b) Central of mass of a body is the point at which the total garvitational torque on the body is zero
(c ) Couple on a body produces both trasnlational and rotation motion in a body
(d) Mechinical advantage greater than one means that small efforts can be used to lift a large load

Options

A. (2) and (4)
B. (1) and (2)
C. (2) and (3)
D. (3) and (4)

Answer

To determine which of the statements are correct, let's analyze each one step by step.

### Step 1: Analyze Statement (a)
**Statement:** Centre of mass of a body always coincides with the centre of gravity of the body.

**Analysis:** This statement is incorrect. The center of mass is a point where the mass of the body can be considered to be concentrated, while the center of gravity is the point where the total weight of the body acts. For uniform gravitational fields and symmetrical bodies, the center of mass and center of gravity may coincide. However, for irregularly shaped objects or in non-uniform gravitational fields, they do not necessarily coincide.

**Conclusion:** Statement (a) is **incorrect**.

### Step 2: Analyze Statement (b)
**Statement:** Centre of mass of a body is the point at which the total gravitational torque on the body is zero.

**Analysis:** This statement is correct. The center of mass is defined as the point where the total torque due to gravitational forces is zero. This means that if you were to apply forces at the center of mass, the object would not rotate.

**Conclusion:** Statement (b) is **correct**.

### Step 3: Analyze Statement (c)
**Statement:** Couple on a body produces both translational and rotational motion in a body.

**Analysis:** This statement is incorrect. A couple consists of two equal and opposite forces acting on a body, which creates a rotational effect without causing any translational motion. Therefore, a couple only produces rotational motion.

**Conclusion:** Statement (c) is **incorrect**.

### Step 4: Analyze Statement (d)
**Statement:** Mechanical advantage greater than one means that small efforts can be used to lift a large load.

**Analysis:** This statement is correct. Mechanical advantage (MA) is defined as the ratio of the load force to the effort force. If MA is greater than one, it indicates that a smaller effort can lift a larger load, which is a fundamental principle of machines.

**Conclusion:** Statement (d) is **correct**.

### Final Conclusion:
The correct statements are:
- Statement (b): Centre of mass of a body is the point at which the total gravitational torque on the body is zero.
- Statement (d): Mechanical advantage greater than one means that small efforts can be used to lift a large load.

### Summary of Correct Statements:
- (b) is correct.
- (d) is correct.