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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