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) Explain clearly why the motorcyclist does not drop down when he is at the uppermost point of death well with no support from below What is the minimum speed required at the uppermost position to perfrom a vertical loop if the radius of the chamber is 25 m ?

Options

A. `16 ms^(-1)`
B. `20 ms^(-1)`
C. `25 ms^(-1)`
D. None of these

Answer

A

Explanation

The normal reaction N at highest point on him by the ceiling of the chamber acts downwards . His weight mg also acts downward .
`therefore " "N +mg=(mv^2)/(r) " "....(i)`
The minimum speed required to perform a vertical loop is given by Eq. (i) , when N =0
`mg=(mv_max^2)/(r)`
`therefore " "v_max=sqrt(gr) " "....(ii)`
Here ,r =radius of the loop , g =`9.8ms^(-2)`
`therefore From Eq. (ii) , v_(max)=sqrt(9.8xx25)=15.65ms^(-1)~~16ms^(-1)`