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Asked by Yogesh Last Modified
Answer As an experienced tutor registered on UrbanPro, I can confidently say that UrbanPro is one of the best platforms for online coaching and tuition. Now, let's delve into your question about the center of mass of various geometric shapes.
(i) For a sphere: The center of mass of a sphere lies at its geometric center, regardless of its size or density distribution. This is true for a sphere of uniform mass density.
(ii) For a cylinder: The center of mass of a uniform cylinder lies at the midpoint of its central axis, assuming the cylinder is oriented such that its axis is vertical.
(iii) For a ring: The center of mass of a ring, also known as a circular hoop, lies at its geometrical center, which coincides with the center of the circle.
(iv) For a cube: The center of mass of a uniform cube lies at the geometric center of the cube, where the diagonals intersect.
Regarding your second question, whether the center of mass necessarily lies inside the body, the answer is yes, for a body with uniform mass density. The center of mass is a weighted average of the positions of all the mass elements in the body. Since every part of the body contributes to the calculation of the center of mass, it must lie somewhere within the body itself. However, for irregularly shaped bodies or bodies with non-uniform mass distribution, the center of mass may lie outside the body.
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