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(a) Centre of gravity (C.G.) of a body is the point at which the weight of the body acts
(b) Centre of mass coincides with the centre of gravity if the earth is assumed to have infinitely large radius
(c) 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.
(d) 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?
(b) Centre of mass coincides with the centre of gravity if the earth is assumed to have infinitely large radius
(c) 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.
(d) 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
(d) and (a)
B
(a) and (b)
C
(b) and (c)
D
(c) and (d)
Detailed Solution
(a) is correct: the centre of gravity is defined as the point through which the resultant weight of the body acts, i.e., the point about which the total gravitational torque is zero.
(c) is not correct in general: treating the whole mass as concentrated at one point works for a spherically symmetric body, but not for a body of arbitrary shape.
The answer accepted in the key pairs (a) with (d), giving '(d) and (a)'.
Note: this key is doubtful. By definition the radius of gyration k is given by $I = Mk^2$ (the distance from the axis at which the whole mass could be concentrated to give the same moment of inertia); it is not the perpendicular distance of the C.G. from the axis, so (d) is strictly false. Statement (b) is true: if the earth's radius were infinitely large, g would be uniform over the body and the centre of gravity would coincide with the centre of mass. On physical grounds the correct pair is (a) and (b); the key of the source PDF is retained here and should be verified.
(c) is not correct in general: treating the whole mass as concentrated at one point works for a spherically symmetric body, but not for a body of arbitrary shape.
The answer accepted in the key pairs (a) with (d), giving '(d) and (a)'.
Note: this key is doubtful. By definition the radius of gyration k is given by $I = Mk^2$ (the distance from the axis at which the whole mass could be concentrated to give the same moment of inertia); it is not the perpendicular distance of the C.G. from the axis, so (d) is strictly false. Statement (b) is true: if the earth's radius were infinitely large, g would be uniform over the body and the centre of gravity would coincide with the centre of mass. On physical grounds the correct pair is (a) and (b); the key of the source PDF is retained here and should be verified.