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  4. A large number of particles are placed around the origin, each at a distance R from the origin. The distance of the center of mass of the system from the origin is

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Q. A large number of particles are placed around the origin, each at a distance $R$ from the origin. The distance of the center of mass of the system from the origin is

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Solution:

As large number of particles is situated at a distance $R$ from the origin. If particles are uniformly distributed and make a circular boundary around the origin, then centre of mass will be at the origin. While if the particles are not uniformly distributed, then centre of mass will lie between particle and origin. This implies the distance between centre of mass and origin is always less than equal to $R$.