Question

Statement-1: Centre of gravity and centre of mass have same physical meaning. Statement-2 : In uniform gravitational field, centre of mass and centre of gravity are at the same point. (1) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement- \(-1\). (2) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (3) Statement-1 is True, Statement-2 is False (4) Statement-1 is False, Statement-2 is True

Short answer

Option (2) is correct.

Step-by-step solution

Understand Statement-1

Statement-1 says that the center of gravity and center of mass have the same physical meaning. Recall that the center of mass is a point representing the mean position of the matter in a body. The center of gravity is the point where the total weight of the body acts. They can be different in a non-uniform gravitational field, but in a uniform gravitational field, they coincide.

Understand Statement-2

Statement-2 says that in a uniform gravitational field, the center of mass and center of gravity are at the same point. This is accurate because, in a uniform gravitational field, the gravitational force acts equally on all parts of the body, making the center of gravity identical to the center of mass.

Evaluate the Statements Together

Both Statement-1 and Statement-2 are true. However, Statement-1 is a general statement about the equivalence of the center of mass and center of gravity, while Statement-2 provides a specific condition (uniform gravitational field) under which they coincide. Statement-2 does not fully explain Statement-1, as Statement-1 assumes a broader context.

Choose the Correct Option

Based on the evaluations, option (2) is correct: 'Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1'.

Key concepts

Uniform Gravitational Field

A uniform gravitational field means that the gravitational force is constant in magnitude and direction at every point within the field. Imagine pushing down uniformly on a sponge; the force you apply at every point is the same.
This concept simplifies calculations since the same gravitational force acts on all parts of an object. Because of this uniformity, an object's center of mass and center of gravity coincide in such a field.
This means we can often treat the entire weight of an object as if it is concentrated at this single point.

• The Earth’s gravitational field is nearly uniform over small regions.
• This idea is fundamental in various physics problems, especially those involving Earth’s surface.

Physics Concepts

Physics helps us understand the rules that govern the universe. Some of the key concepts that tie into this exercise are center of mass and center of gravity.
The center of mass is a point that represents the average position of all the mass in an object. For example, when you spin a baseball bat, it appears to rotate around this point.
The center of gravity is the point where the total weight of the body appears to act. In real-world applications:

• Engineers use these concepts to ensure stability in buildings and vehicles.
• Athletes and performers use their knowledge to maintain balance and control.

Knowing the difference and the conditions under which they coincide is crucial for solving many physics problems.

IIT JEE Preparation

Preparing for the IIT JEE requires a deep understanding of fundamental concepts. In the context of problems about the center of mass and center of gravity:
Make sure you thoroughly understand the definitions. Know that while they can coincide, the center of mass and center of gravity are different concepts.
Practice problems involving different gravitational fields.

• Focus on both uniform and non-uniform fields.
• Understand how these fields affect the position of centers of mass and gravity.

Using this knowledge, you can tackle various types of questions that may appear in the examination.