Question

Question: (a) center of gravity (CG) of a body is a point at which the weight of the body acts.
(b) The Center of mass coincides with the center of gravity if the earth is assumed to have an infinitely large radius.
(c) To evaluate the gravitational field intensity due to anybody at an external point, the entire mass of the body can be considered to be concentrated at its CG.
(d) The radius of gyration of anybody rotation about an axis is the length of the perpendicular dropped from the CG of the body to the axis.
Which of the following pairs of statements is correct?
A. (a) and(c)
B. (a) and (b)
C. (b) and (c)
D. (c) and(d)

Answer 1

center of gravity (CG) of a body is a point at which the entire weight of the body concentrates.Centre of the mass (CM) coincides with the center gravity (CG) only when the mass is distributed uniformly over the body. The gravitational field acting on the body can be calculated by considering the body as a point mass.

Complete step-by-step answer:
The Centre of gravity of a body is defined as the point where the whole weight of the body is supposed to act. A body supported at its center of gravity remains balanced and it is in mechanical equilibrium. The reaction R at the point of support is equal and opposite to the total weight MG of the body. Hence, there is a translational equilibrium. Also, the total gravitational torque on the body at the center of gravity is zero. Hence, there is a rotational equilibrium. The center of gravity of the body coincides with the center of mass in uniform gravity (constant value of acceleration due to gravity) or gravity-free space.
the remaining two statements are wrong.
The radius of gyration of a body about an axis is defined as the distance from the axis of rotation to the mass point whose mass is equal to the mass of the whole body and whose moment of inertia is equal to the moment of inertia of the whole body about the same axis.
Correct options are (a) and (b)
Additional information:
1. The moment of inertia resembles mass. In the rotation of a body about a fixed axis, the moment of inertia plays a similar role as mass does in linear motion.
2. It is a measure of inertia of the body for rotational motion (rotational inertia).
3. The moment of inertia of a body about a given axis of rotation is defined as the sum of the product of the masses of the particles in the body and square of the distance from the axis of rotation.
Note:
1. A rigid body is said to be in mechanical equilibrium if its linear momentum, as well as angular momentum, are not changing with time.
2. The vector sum of the forces acting on the rigid body is zero.
3. The vector sum of the torque on the rigid body is zero.