Question

(1) Centre of gravity of a body is the point at which the weight of the body acts. (2) Centre of mass coincides with the centre of gravity if the earth is assumed to have infinitely large radius. (3) To evaluate the gravitational field intensity due to any body at an external point, the entire mass of the body can be considered to be concentrated at its centre of gravity. (4) The radius of gyration of any body rotating about an axis is the length of the perpendicular drawn from the centre of gravity of the body to the axis. Which one of the following pairs of statements is correct?

• (1) and (4)
• (1) and (2)
• (2) and (3)
• (3) and (4)

Answer 1

The Correct Option is A

To determine which pair of statements is correct regarding the concepts of center of gravity, center of mass, gravitational field intensity, and radius of gyration, we need to evaluate each statement one by one:

1. Centre of gravity of a body is the point at which the weight of the body acts.
   This statement is correct. The center of gravity is defined as the point at which the entire weight of a body can be considered to act, regardless of its position.
2. Centre of mass coincides with the centre of gravity if the earth is assumed to have infinitely large radius.
   This statement is also correct. If the Earth were assumed to have an infinitely large radius, the gravitational field would be uniform, causing the center of mass to coincide with the center of gravity.
3. To evaluate the gravitational field intensity due to any body at an external point, the entire mass of the body can be considered to be concentrated at its centre of gravity.
   This statement is incorrect. When evaluating gravitational field intensity, we normally consider the center of mass rather than the center of gravity for simplification, especially in cases where the gravitational field is not uniform.
4. The radius of gyration of any body rotating about an axis is the length of the perpendicular drawn from the centre of gravity of the body to the axis.
   This statement is incorrect. The radius of gyration is not defined as the perpendicular distance from the center of gravity to the axis of rotation. Instead, it is a hypothetical distance which, when squared and multiplied by the mass of the body, gives the moment of inertia.

After evaluating each statement, the correct pair of statements is (1) and (2), not (1) and (4).

Conclusion: Although the given answer says (1) and (4), upon evaluation, the correct choice should be (1) and (2).