(1) Centre of gravity (C.G.) 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 enti…

Question

(1) Centre of gravity (C.G.) 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 C.G.
(4) The radius of gyration of any body rotating about an axis is the length of the perpendicular drawn from the C.G. of the body to the axis.
Which one of the following pairs of statements is correct?

Accepted Answer

(2) (1) and (2). Idea: test each statement separately against its own definition. (1) The centre of gravity is by definition the point through which the resultant weight acts, so (1) is correct. (2) A body is small compared with the Earth only because the Earth is large; let the radius grow without limit and g becomes strictly uniform over the body, which is exactly the condition for the centre of gravity to sit at the centre of mass. So (2) is correct. (3) Replacing a body by a point mass at one point reproduces the external field only for a spherically symmetric body, not for any body. So (3) is wrong. (4) I=MK² defines K=√I/M, which is not the perpendicular distance from the centre of gravity to the axis. So (4) is wrong. The correct pair is (1) and (2).

Step-by-step solution

Why the other options are wrong