Question

A space station consists of two donut-shaped living chambers, A and B, that have the radii shown in the figure. As the station rotates, an astronaut in chamber A is moved 2.71 x 102 m along a circular arc. How far along a circular arc is an astronaut in chamber B moved during the same time?

Answer 1

Answer:

A Space Station Consists Of Two Donut-shaped Living Chambers, A And B, That Have The Radii Shown In The Drawing. As The Station Rotates, An Astronaut In Chamber A Is Moved 2.80 102 M Along A Circular Arc.

Answer 2

Answer:

the distance moved by an astronaut in chamber B along a circular arc is $9.35\times 10^{2}m$.

Explanation:

Given radius of chamber A, $R_{A} =3.2\times 10^{2} m$

         radius of chamber B, $R_{B} =1.1\times 10^{3} m$

Distance moved by an astronaut in chamber A along a circular arc,

                                             $d_{A} =2.71\times10^{2} m$

Distance travelled along a circular arc, $d=r\theta$

                      $\implies d_{A} =r_{A}\theta_{A} \implies 2.71\times 10^{2} =3.2\times 10^{2} \times \theta_{A}$

                                                 $\implies \theta_{A} = \frac{2.71\times 10^{2}}{3.2\times 10^{2} }=0.85$

Angle of rotation of both the chambers must be equal

                         i.e., $\theta_{A} = \theta_{B}$

Hence, the distance moved by an astronaut in chamber B is

                        $d_{B} =1.1\times 10^{3} \times 0.85$

                             $= 9.35\times 10^{2}m$

Therefore, the distance moved by an astronaut in chamber B along a circular arc is $9.35\times 10^{2}m$.