The Question is from neet-physics , and it was created by the author SUBHANI

Question

Which of the following statements are correct?
 1) Centre of mass of body always coincides with the centre of gravity of the body.
 2) Central mass of a body is the point at which the total gravitational torque on the body is zero.
 3) A couple on a body produce both translational and rotational motion in a body.
 4) Mechanical advantage greater than one means that small effort can be used to lift a large load.

SUBHANI · Accepted Answer

## CORE INFORMATION
✓ **Answer**: B
## CONCEPT FRAMEWORK
	**Primary Concept**: Understanding of center of mass, center of gravity, torque, couples, and mechanical advantage.
	**Related Topics**: Rotational motion, Equilibrium, Simple machines.
	**Prerequisites**: Basic definitions and understanding of the concepts listed above.
## SOLUTION PATHWAY
**Given Information**:
	Four statements regarding center of mass, center of gravity, torque, couples and mechanical advantage.
	Need to identify the correct statements.
**Method & Steps**:
	1. Analyze statement 1: Center of mass and center of gravity coincide when the gravitational field is uniform. They don't always coincide. Hence, this statement is incorrect.
		Reasoning: Center of mass is a property of the object's mass distribution, while center of gravity is the point where the net gravitational force acts. If the gravitational field is non-uniform, these points won't coincide.
		Formula/Rule: Center of mass formula:  $\vec{r}_{CM} = \frac{\sum m_i \vec{r}_i}{\sum m_i}$ Center of gravity is calculated similarly, but using weight instead of mass.
	2. Analyze statement 2: The center of gravity (not 'central mass') is the point where the net gravitational torque is zero. This statement is correct.
		Reasoning: Torque is the rotational force. If the net torque due to gravity is zero, the object won't rotate under gravity, defining the center of gravity.
		Formula/Rule: Torque = Force x lever arm.  For gravitational torque, Force = weight.
	3. Analyze statement 3: A couple produces pure rotational motion and no translational motion. Hence, the statement is incorrect.
		Reasoning: A couple consists of two equal and opposite forces that produce a torque but no net force.
		Formula/Rule: Torque due to a couple = Force * distance between the forces.
	4. Analyze statement 4: Mechanical advantage > 1 means the load lifted is larger than the effort applied. This is correct.
		Reasoning: Mechanical advantage is the ratio of load to effort. A value greater than 1 indicates a force multiplier.
		Formula/Rule: Mechanical Advantage = Load / Effort
	5. Identify correct options: Statements 2 and 4 are correct.
		Result: Correct statements are (b) and (d).
		Verification:  The analysis of each statement leads to the conclusion that only (b) and (d) are correct.
## OPTION ANALYSIS
[A] :x: Incorrect. Statement (c) is not correct.
[B] ✓: Correct. Statements (b) and (d) are correct.
[C] :x: Incorrect. Statement (a) is not correct.
[D] :x: Incorrect. Statement (c) is not correct.
## LEARNING AIDS
	**Common Mistakes**:
		1. Confusing center of mass and center of gravity: They only coincide in uniform gravitational fields.
			How to avoid: Understand the definitions and the conditions under which they are different.
		2. Misunderstanding the effect of a couple: A couple produces only rotation, not translation.
			How to avoid: Remember that a couple has no net force, only a torque.
	**Quick Tips**:
		1. Center of Gravity: Think of it as the point where an object would balance.
		2. Mechanical Advantage: A number greater than one implies a force amplifier.

SUBHANI · Answer

(c) and (b)

SUBHANI · Answer

The correct Option is "(b) and (d)"

SUBHANI · Answer

(a) and (b)

SUBHANI · Answer

(b) and ( c)

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