Question

The centre of mass of an extended body on the surface of the earth and its centre of gravity

• A. can never be at the same point
• B. are always at the same point for any size of the body
• C. centre of mass coincides with centre of gravity of a body if the size of the body is negligible as compared to the size (or radius) of the earth
• D. are always at the same point only for spherical bodies

Answer 1

The Correct Option is C

The center of mass and the center of gravity are related concepts but have key differences:

Center of Mass:

• The center of mass of an extended body is the point where the entire mass of the body can be considered to be concentrated.
• It is the average position of all the individual particles' masses that make up the body.
• The center of mass is determined based on the distribution of mass within the object.

Center of Gravity:

• The center of gravity is the point where the force of gravity can be considered to act on the body.
• In a uniform gravitational field, the center of gravity coincides with the center of mass.
• In non-uniform gravitational fields, the center of gravity may differ slightly from the center of mass.

In summary: The center of mass is related to mass distribution, while the center of gravity is related to the distribution of the gravitational force. In most practical situations where gravity is uniform, the two points coincide.