The centre of mass of two particles system lies

Statement-1 : The centre of mass of a two particle system lies on the line joining the two particles, being closer to the heavier particle. Statement-2 : Product of mass of one particle and its distance from centre of mass is numerically equal to product of mass of other particle and its distance from centre of mass.

Where does the centre of mass of a two particle system lie, if one particle ismore massive than the other ?

find moment of inertia about an axis yy which passes through the centre of mass of the two particle system as shown

Write an expression for the centre of mass of& two partide system

The centre of mass of three particles of masses 1kg, 2 kg and 3kg lies at the point (3m, 3m, 3m). Where should a fourth particle of mass 4 kg be positioned so that the centre of mass of the four particle system lies at the point (1m, 1m, 1m)?

Obtain an expression for the position vector of centre of mass of a two particle system.

(i) A regular polygon has 2016 sides and r is the radius of the circle circumscribing the polygon. Particles of equal mass are placed at 2015 vertices of the polygon. Find the distance of the centre of mass of the particle system from the centre of the polygon. (ii) In the last problem you have been asked to remove any one particle from the system so that the centre of mass of the remaining 2014 particles lies farthest from the geometrical centre of the polygon. Which particle will you remove ?

Find the distance between centre of gravity and centre of mass of a two particle system attached to the ends of a light rod. Each particle has same mass. Length of the rod is R, where R is the radius of earth.

The coordinates of the centre of mass of a system of three particles of mass 1g,2g and 3g are (2,2,2). Where should a fourth particle of mass 4 g be positioned so that the centre of mass of the four particle system is at the origin of the three-dimensional coordinate system ?