Question

(i) Centre of gravity (C.G) of a body is the point at which the weight of the body acts.
(ii) Centre of mass coincides with the centre of gravity if the earth is assumed to have an infinitely large radius.
(iii) 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 C.G.
(iv) The radius of gyration of any body rotating about an axis is the length of the perpendicular dropped from the C.G of the body to the axis
Which one of the following pairs of statements is correct?
A. (iv) and (i)
B. (i) and (ii)
C. (ii) and (iii)
D. (iii) and (iv)

Answer 1

Hint: First let us see what centre of gravity and centre of mass is:
Centre of gravity: The point at which weight is uniformly distributed and both sides are in equilibrium is the centre of gravity (CG) of an object. A human's centre of gravity will change when he takes on various positions, but in many other objects, it's a fixed spot.
Centre of mass: A location specified relative to an object or system of objects is the centre of mass. It is the average location, weighted according to the masses, of all the parts of the system.

Complete answer:
A body's centre of gravity is the point at which the weight of the body functions. The centre of gravity is the point at which the weight distribution in both directions is equal and depends on the gravitational field.
Hence, statement (i) is correct.
If the gravitational field remains uniform over space , i.e. the field is regardless of the spatial location, the body's centre of mass and centre of gravity coincide in that space.
Hence, statement (ii) is wrong.
It is possible to quantify the gravitational field at any extreme level, assuming it is a point mass.
Hence, we can see that statement (iii) is incorrect.
A body's centre of gravity is the point at which the weight of the body functions and the gyration radius of the body that spins around an axis is the length of the perpendicular dropped from the body's CG to the axis. This is a loop equation, because the particle is taking a circular direction.
Hence, statement (iv) is correct.

So, the correct answer is “Option A”.

Note:
We may be confused between centre of mass and centre of gravity but centre of mass is the distribution of mass and centre of gravity is the distribution of weight. Also centre of mass does not depend on the gravitational field and centre of gravity does.