Question #89bdd

Jan 21, 2017

Here it is given that the space station is spinning with an angular speed ($\omega$) of 2 rpm

So $\omega = 2 r p m = \frac{2 \times 2 \pi}{60} \text{radian/s"=pi/15"rad/s}$

So centripetal acceleration produced $a = {\omega}^{2} R$, where R is the the radius of the space station. As per given condition this acceleration $a$ will be equal to the artificial acceleration due to gravity $g = 10 \text{m/} {s}^{2}$ experienced by an astronaut.

So $g = {\omega}^{2} R$

$R = \frac{g}{\omega} ^ 2 = \frac{10}{\frac{\pi}{15}} ^ 2 m = \frac{2250}{\pi} ^ 2 m \approx 228 m$