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?

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

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

The coordinate of the centre of mass of a system as shown in figure : -

The coordinate of the centre of mass of a system as shown in figure : -

All the particles of body are situated at a distance R from the origin. The distance of the centre of mass of the body from the origin is also R. Is this statement true or false?

All the particles of body are situated at a distance R from the origin. The distance of the centre of mass of the body from the origin is also R. Is this statement true or false?

The x and y coordinates of the center of mass of the three-particle system shown below are :

The x and y coordinates of the center of mass of the three-particle system shown below are :