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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