NEET Sample Paper NEET Sample Test Paper-16

  • 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

    Correct Answer: B

    Solution :

    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).            

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