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NEET Sample Paper NEET Sample Test Paper-87

  • question_answer
    A body moves in a circular orbit of radius r under the action of a central force. Potential due to the central force is given by V(r) = kr (k is a positive constant). Period of revolution of the body is proportional to:

    A) \[{{r}^{1/2}}\]            

    B)        \[{{r}^{-1/2}}\] 

    C) \[{{r}^{-3/2}}\]                       

    D)        \[{{r}^{-5/2}}\]

    Correct Answer: A

    Solution :

    [a] \[U=mV=kmr.\] Force, F \[=-\frac{dU}{dr}=-km\] Now, \[\frac{m{{v}^{2}}}{r}=km\]\[\therefore \]\[v\propto {{r}^{1/2}}\] \[\therefore \] \[T=\frac{2\pi r}{v}=\frac{2\pi r}{c{{r}^{1/2}}}\] \[\Rightarrow \] \[T\propto {{r}^{1/2}}\]


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