Question:

If three particles of masses 2kg, 1kg and 3 kg are placed at comers of an equilateral triangle of perimeter 6m then the distance of center of mass which is at origin of particles from 1kg mass is (approximately) (Assume 2kg on x-axis )

Updated On: Jul 6, 2022
  • $\sqrt6m$
  • $\sqrt2m$
  • $\frac{1}{\sqrt2}m$
  • 2m
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The Correct Option is B

Solution and Explanation

Co-ordinates o f 1 kg, 2 kg, 3 kg are (0,0), (2,0), (1, $\sqrt{3}$ ) respectively $X_{cm} = \frac{\sum m_i x_i}{\sum m_i} ; Y_{cm} = \frac{\sum m_i y_i}{\sum m_i} r_{cm} = \sqrt{X^2_{cm} + Y^2_{cm}}$
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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.