Question

Give the location of the centre of mass of a (i) sphere, (ii) cylinder, (iii) ring, and (iv) cube, each of uniform mass density. Does the centre of mass of a body necessarily lie inside the body?

Answer 1

Heya!!

# Center of Mass :- The center of Mass is a position defined relative to an object or system of objects . It is the average position of all the parts og the system weighted according to their masses.
Or simply we can say --- a point where we can say that the whole mass of a body or system is concentrated .


Now we will see the location of centre of Mass of the following :
1) Sphere : It is located on the center of the Sphere
2) Cylinder : It is located on the center of it's axis .
3) ring : it is located on the center of ring .
4) Cube : It is located where all the diagonals intersects .

In all cases as the mass distribution is uniform thus the centre of Mass lie on their symmetric centres.


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Yes centre of Mass can lie outside of the body or system too .
As it depends upon the configuration and composition of the System or body .



I hope it will be helpful.

Answer 2

(A) centre of mass of sphere lies at the geometrical centre .
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(B) centre of mass of cylinder lies at its geometrical centre.
e.g at the mid point of axis of symmetry.
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(C) centre of mass of ring lies at its geometrical centre.

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(D) centre of mass of cube lies at geometrical centre. I mean centre of mass lies at the point of intersection of diagonals .
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