Question:

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

Updated On: Apr 27, 2024
  • equal to R
  • less than equal to R
  • greater than R
  • greater than equal to
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The Correct Option is B

Solution and Explanation

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 $R$.
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Concepts Used:

Center of Mass

The center of mass of a body or system of a particle is defined as a point where the whole of the mass of the body or all the masses of a set of particles appeared to be concentrated.

The formula for the Centre of Mass:

Center of Gravity

The imaginary point through which on an object or a system, the force of Gravity is acted upon is known as the Centre of Gravity of that system. Usually, it is assumed while doing mechanical problems that the gravitational field is uniform which means that the Centre of Gravity and the Centre of Mass is at the same position.