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Question
For which of the following does the centre of mass lie outside the body?
Options
A pencil
A shotput
A dice
A bangle
Solution
A bangle
Explanation:
The Center of mass of a system (body) is a point that moves as though all the mass were concentrated there and all external forces were applied there.
Important points about the center of Mass:
(i) The position of center of mass is independent of the coordinate system chosen.
(ii) The position of center of mass depends upon the shape of the body and the distribution of mass.
Example: The center of mass of a circular disc is within the material of the body while that of a circular ring is outside the material of the body.
(iii) We can imagine a rigid body also as a system of masses and hence every rigid body has a center of mass. In the case of a regularly shaped uniform rigid body, center of mass is simply the geometric centre of the body.
A bangle is in the form of a ring as shown in the diagram below. We know that the position of center of mass depends upon the shape of the body and the distribution of mass. So, out of four given bodies, the centre of mass lies at the centre, which is outside the body (boundary) whereas in all other three bodies it lies within the body because they are completely solid.
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