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Laws Of Motion

Question
CBSEENPH11016988

You may have seen in a circus a motorcyclist driving in vertical loops inside a death well (a hollow spherical chamber with holes, so that the spectators can watch from outside). Explain clearly why the motorcyclist does not drop down when he is at the uppermost point, with no support from below. What is the minimum speed required at the uppermost position to perform a vertical loop if the radius of the chamber is 25 m?

Solution
The motorcyclist does not drop down when he is at the uppermost point if centrifugal force on motorcyclist is greater or equal to the weight of motorcyclist.
i.e.
              fraction numerator m v squared over denominator R end fraction greater or equal than m g 
rightwards double arrow          v greater or equal than square root of r g end root 
The minimum speed of motorcyclist not to fall from uppermost point is given by 
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Here, given
              r = 25m,            g equals 9.8 space m divided by s squared 
∴           v subscript m i n end subscript equals square root of 25 cross times 9.8 end root space equals space 15.7 space straight m divided by straight s