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?
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In all the four cases, as the mass thickness is uniform, centreof mass is situated at their individual geometrical focuses.
No, it isn't important that the focal point of mass of a body should lie on the body. For instance, in the event of a round ring, focus of mass is at the focal point of the ring, where there is no mass .
No, it isn't important that the focal point of mass of a body should lie on the body. For instance, in the event of a round ring, focus of mass is at the focal point of the ring, where there is no mass .
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Hey mate,
● Explained Answers-
I. Here, each object has uniform mass density, thus
a) Sphere-
Center of mass lies at geometrical centre of the sphere.
b) Cylinder-
Center of mass lies at midpoint of axis of symmetry.
c) Ring-
Center of mass lies at geometrical centre of the ring.
d) Cube-
Center of mass lies at point of intersection of diagonals.
II. No.
Centre of mass needn't be in the body. It's just where mass of the body is supposed to be concentrated for theoretical purposes.
In hollow objects (sphere, cube, etc), ring center of mass is not within the body.
Hope that solved your questions...
● Explained Answers-
I. Here, each object has uniform mass density, thus
a) Sphere-
Center of mass lies at geometrical centre of the sphere.
b) Cylinder-
Center of mass lies at midpoint of axis of symmetry.
c) Ring-
Center of mass lies at geometrical centre of the ring.
d) Cube-
Center of mass lies at point of intersection of diagonals.
II. No.
Centre of mass needn't be in the body. It's just where mass of the body is supposed to be concentrated for theoretical purposes.
In hollow objects (sphere, cube, etc), ring center of mass is not within the body.
Hope that solved your questions...
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