Question

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

Answer 1

correct option is b. 31.3 m/s

Step-by-step 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

`(a2)/(a1) = (v2)/(v1)` .....................1

put here value

`(2)/(1) = (v2)/(22.1)`

solve it

v2 =
`√(2 )` × 22.1

v2 = 31.25 m/s

so correct option is b. 31.3 m/s