Centre of mass is point

Centre of mass is at point X (1,1,1) when system consists of particles of masses 2, 3, 4 and 5 kg. If the centre of mass shifts to point Y (2, 2, 2) on removal of the mass of 5 kg. What was its position ?

A spherical body of radius R rolls on a horizontal surface with linear velociltly v . Let L_(1) and L_(2) be the magnitudes of angular momenta of the body about centre of mass and point of contact P . Then:

A spherical body of radius R rolls on a horizontal surface with linear velociltly v . Let L_(1) and L_(2) be the magnitudes of angular momenta of the body about centre of mass and point of contact P . Then:

A uniformly thick plate in the shape of an arrow head has dimensions as shown. Find the distance of centre of mass from point O (in cm)

A uniformly thick plate in the shape of an arrow head has dimensions as shown. Find the distance of centre of mass from point O (in cm)

A uniformly thick plate in the shape of an arrow head has dimensions as shown. Find the distance of centre of mass from point O (in cm)

A square lamina of side a and a circular lamina of diameter a are placed touching each other as shown in figure. Find distance of their centre of mass from point O, the centre of square.