If all the particle of a system lie in a cube is it necessary that the centre of mass be in the cube?

The centre of mass is defined as vecR=1/Msum_im_ivecr_i . Suppose we define centre of charge as vecR_c=1/Qsum_iq_Ivecr_i where q_i represents the ith charge placed at vecr_i and Q is the total charge of the sytem a. Can a centre of charge of two charge system be outside the line segment joining the charges? b. If all the charges of a system are in X-Y plane? c. If all the charges of a system lie in a cube, is it necessary that the centre of charge be in the cube?

If all the particle of a system lie in X-Y plane is it necessary that the centre of mass be in X-Y plane?

If all the particles of a system lie in y-z plane, the x-coordinate of the centre of mass will be zero. Is this statement true or false?

Calculate centre of mass of the system

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 ?

The rate of change of angular momentum of a system of particles about the centre of mass is equal to the sum of external torque about the centre of mass when the centre of mass is :

If a sphere of radius 3 is inscribed in a cube such that it is tangent to all six faces of the cube, the volume contained outside the sphere and inside the cube is

Consider a system of two particles having masses m_(1) and m_(2) . If the particle of mass m_(1) is pushed towards the centre of mass of particles through a distance d , by what distance would the particle of mass m_(2) move so as to keep the mass centre of particles at the original position?

Consider a system of two particles having masses 2kg and 5 kg the particle of mass 2 kg is pushed towards the centre of mass of particles through a distance 5 m,by what distance would particle of mass 5kg move so as to keep the centre of mass of particles at the original position?

Centre of mass of three particles of masses 1 kg, 2 kg and 3 kg lies at the point (1,2,3) and centre of mass of another system of particles 3 kg and 2 kg lies at the point (-1, 3, -2) . Where should we put a particle of mass 5 kg so that the centre of mass of entire system lies at the centre of mass of first system ?