Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

The center of mass of rigid body lies-
A) inside the body
B) outside the body
C) neither A nor B
D) either A or B

Answer
VerifiedVerified
525.6k+ views
Hint
The center of mass depends only on the shape of body and mass distribution of the body. To this end, think of where the center of mass of hollow objects lie given their mass distribution is circumferential.

Complete step by step solution
Let us begin by understanding what center of mass is and on what factors it depends.
The center of mass of the system is defined at the point at which the whole mass of the system appears to be concentrated. Any external force applied will act on this point. In the case of rigid bodies, the center of mass is fixed in relation to the body, and if the body has uniform density, it will be located at the centroid.
The position of center of mass of body depends upon two factors,
(i) Shape of the body
(ii) Distribution of the mass
These are the deciding factors in determining whether the center of mass lies outside or inside the body. Here, inside and outside means if the center of mass lies where we can find the physical structure of the body, we say it inside while if it lies within the space that the body is present in but not on its physical structure then we say it lies outside the body.
So, a solid rigid symmetrical body has a center of mass lying inside the body.
However, the center of mass not necessary lies within the body when the object loses its geometric symmetricity as in a case of boomerang, where the center of mass lies outside owing to its uneven mass distribution due to its shape
The object is hollow or its mass distributed entirely on its circumference as in a case of ring or concentric circle. For these, the center of mass will be at kits center, where there is no mass present.
Hence, option D is correct, center of mass can lie inside or outside the body.

Note
Do not get confused between the center of mass and center of gravity. Center of mass is the point at which distribution of mass is equal in all directions whereas center of gravity is the point where distribution of weight is equal in all directions. Center of mass arises from the geometric behaviour of an object and hence does not depend on the gravitation field whereas the center of gravity arises from the physical behaviour of the object and depends on the gravitational field acting on it.