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KVPY Sample Paper KVPY Stream-SX Model Paper-4

  • question_answer
    You may have seen in a circus a motorcyclist driving in vertical loops inside a 'death well' (a hollow spherical chamber with holes, so the spectators can watch from outside). What is the minimum speed required at the uppermost position of motorcyclist to perform a vertical loop, if the radius of the chamber is 25 m?

    A) \[15.65 m/s\]     

    B) \[12.48 m/s\]

    C) \[14.56m/s\]                  

    D) \[18.48m/s\]

    Correct Answer: A

    Solution :

    [a]
    When the motorcyclist is at the uppermost point of the death well, then weight of the cyclist as well as the normal reaction R of the ceiling of the chamber is in downward direction. These forces are balanced by the outward centrifugal force acting on the motorcyclist.
    \[\therefore \]      \[R+mg=\frac{m{{v}^{2}}}{r}\]
    Where, v = speed of the motorcyclist
    \[m\]= Mass of (motor cycle+ driver)
    r = radius of the death well
    As the forces acting on the motorcyclist are balanced, therefore motorcyclist does not fall sown.
    The minimum speed required to perform a vertical loop is given by \[\operatorname{mg}=\frac{m{{v}^{2}}_{\min }}{r}\]
    (\[\because \] in this case weight of the object = centripetal force)
     \[\therefore \]\[{{v}_{\min }}=\sqrt{rg}\]
    \[=\sqrt{25\times 9.8}=15.65\operatorname{m}/s\]          


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