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प्रश्न
A motorcyclist (as a particle) is undergoing vertical circles inside a sphere of death. The speed of the motorcycle varies between 6 m/s and 10 m/s. Calculate the diameter of the sphere of death. How much minimum values are possible for these two speeds?
उत्तर
Given:
`"v"_"top"` = 6 m/s,
`"v"_"bot"` = 10 m/s,
g = 10 m/s2
To find:
- the diameter of the sphere
- minimum values are possible for the two speeds
Solution:
`"v"_"bot"^2="v"_"top"^2 + 4"gr"`
∴ r = `("v"_"bot"^2-"v"_"top"^2)/(4"g")`
`=((10)^2-(6)^2)/(4xx10)=64/40`
= 1.6m
The diameter of the sphere of death = 3.2m.
(ii) `"v"_"min"=sqrt"gr"` at the top.
∴ `"v"_"min"=sqrt(10xx1.6)=sqrt16` = 4 m/s
The corresponding minimum speed at the bottom
= `sqrt(5"gr")`
`=sqrt(5(10)(1.6))`
`=sqrt80`
`=4sqrt5`m/s
The required minimum values of the speeds are 4 m/s and `4sqrt5` m/s.
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