• # 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) $18.48m/s$

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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