Question

The centre of mass of the body:
A) Lies always outside of the body
B) May lie within, outside, on the surface of the body
C) Lies always inside the body
D) Lies always on the surface of the body

Answer 1

Hint: Remember, the position of a body’s centre of mass depends on the physical condition and appearance of that particular object. The distribution of the mass and the shape of the body determines the position of centre of mass. To this end, think about the hollow object’s centre of mass would lie, as their mass distribution is entirely circumferential.

Complete step by step solution:
Let’s discuss the centre of mass of a body and what all properties determine the centre of mass.
The centre of mass of a body is the point at which the whole mass of the body appears to be concentrated. Generally the centre of mass lies inside the body but the position may change. Centre of mass depends on the shape and its mass distribution for a continuous distributed object.
The center of mass need not lie within the body. This happens when the body does not have a geometrical symmetricity. When we consider the case of the center of mass of boomerang, it lies outside the body. Because of the shape and curves of the body of the boomerang, it has an asymmetrical distribution of mass.

For a body with constant density and an axis of symmetry, the center of mass lies on this axis. For example, a circular cylinder of constant density has its center of mass on the axis of the cylinder.

Thus the final answer is option (B) The centre of mass may lie within, outside, on the surface of the body.

Note: Many people assume that the terms centre of mass and centre of gravity are the same, but this is not the case. So there is a chance of getting confused between the centre of mass and the centre of gravity. The centre of gravity is referred to as the point on which the distribution of weight is equal in all directions. It arises from the physical behavior of the body and depends on the gravitation. The centre of gravity and centre of mass of an object are in the same position only if the gravitational field in which the object exists stays uniform.