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A space station in the shape of a 100 m-diameter (50m radius) wheel is spinning so as to impart a linear tangential speed of 22.1 m/s to a point on its outmost wall, thereby providing an artificial gravity of 1g. What should be the tangential speed to increase the artificial gravity to 2 g?

a. 44.2 m/s
b. 31.3 m/s
c. 88.4 m/s
d. 27.8 m/s
e. 177 m/s

Respuesta :

Answer:

correct option is b. 31.3 m/s

Explanation:

given data

artificial gravity a1 = 1 g

artificial gravity a2 = 2 g

diameter = 100 m

radius  r= 50 m

speed v1 = 22.1 m/s

solution

As acceleration is  ∝ v²

so we can say

[tex]\frac{a2}{a1} = \frac{v2}{v1}[/tex]    .....................1

put here value

[tex]\frac{2}{1} = \frac{v2}{22.1}[/tex]  

solve it

v2 = [tex]\sqrt{2 }[/tex] × 22.1

v2 = 31.25 m/s

so correct option is b. 31.3 m/s