• # question_answer 6) A small sphere of radius R held against the inner surface of a smooth spherical shell of radius 6R as shown in the figure. The masses of the shell and small spheres are 4M and M, respectively. This arrangement is placed on a smooth horizontal table. The small sphere is now released. The x-coordinate of the center of the shell when the smaller sphere reaches the other extreme position is A) R                     B) 2R                   C) 3R                D)      4R

Initially $x-$coordinate of center of mass is: ${{x}_{1}}=\frac{(4M)(0)+M(5R)}{4M+M}=R$             (1) Let ${{x}_{0}}$be the x-coordinate of shell when the small sphere reaches the other extreme position. Then finally c-coordinate of center of mass is ${{x}_{f}}=\frac{4M({{x}_{0}})+M({{x}_{0}}-5R)}{4M+M}$ $={{x}_{0}}-R$                                              (2) All the surfaces are smooth, therefore, center of mass will not move in $x-$direction $\therefore$${{x}_{1}}={{x}_{f}}$ or         $R={{x}_{0}}-R$ or         ${{x}_{0}}=2R$ Hence, the correction option is (b).