Three identical spheres each of diameter 2 3 ~m are kept on a horizontal surface such that each sphere touches the other two spheres. If one of the sphere is removed, then the shift in the position of the centre of mass of the system is

Step-by-step solution

The centre of mass of the spheres is given by x_ CM = m₁ x₁+m₂ x₂+m₃ x₃ m₁+m₂+m₃ As the spheres are identical, aligned x_ CM & = m 3 m (0+2 3 + 3 ) & = 3 3 3 = 3 aligned Similarly, aligned y_ CM & = m 3 m (y₁+y₂+y₃ ) & = (0+0+3) 3 =1 aligned So, the centre of mass, C_ CM =( 3 , 1) If one sphere is removed (say C ), then aligned & x_ CM ^ = 0+2 3 2 = 3 & y_ CM ^ =0 aligned So, C_ CM ^ =( 3 , 0) Hence, the centre of mass shifted by 1 ~m in -y direction. The correct option is (b).