Hey....mind ur language...
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?
Answers
Answer:
(i) center of mass of sphere is always at the center of the sphere.
(ii)center of mass for a uniform, regular cylindrical structure, the centre of gravity will be at its body centre, that is the middle of the cylinder. For a cylinder, the centre of the body will be at the centre of its axis.
(iii)center of mass of ring lies at its center.
center of mass of cube lies at its geometric center . The geometric center of a cube is the point of intersection of cube's diagonals.
(iv) For each and every uniform figure, which has uniform mass density, the center of mass will lie on the point where the symmetrical axis intersects with another symmetrical axis.
Symmetrical axis are lines drawn on an object through which when we cut the object we get two parts of the object exactly symmetrical to each other.
It is not necessary that the center of mass of the body will lie on the body; it can lie outside the body also.
Answer:
In all the four cases, as the mass density is uniform, centre of mass is located at their respective geometrical centres.
i) Sphere - Centre of Sphere
ii) Cylinder - Middle Point on axis of cylinder
iii) Ring - At centre of ring (Outside the ring)
iv) Cube - At point of intersection of diagnols
No, it is not necessary that the centre of mass of a body should lie on the body. For example, in case of a circular ring, centre of mass is at the centre of the ring, where there is no mass.