###### System of Particle and Rotational Motion – Solutions

**1) Give the location of the centre of mass of a (1) sphere, (2) cylinder, (3) ring, and (4) cube, each of uniform mass density. Does the centre of mass of a body necessarily lie inside the body?**

Solution:

(1) For a sphere, the centre of mass is located at its geometrical centre.

(2) For a cylinder, the centre of mass is located at the midpoint of its natural axis (geometrical axis).

(3) For a ring, the centre of mass is located at its centre. No, it is not necessary that the centre of mass should lie inside the body.

(4) For a cube, the intersecting point of its space diagonals coincides with the location of its centre of mass.

In all these cases, the geometrical centre coincides with the location of the centre of mass. The centre of mass of a body need not always lie inside the body. For example, in case of a ring, the CM lies outside.

**2) In the HC1 molecule, the separation between the nuclei of the two atoms is about 1.27 A (1 A = 10 ^{-10} m).**

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