In a hypothetical ring shaped satellite rotating in space, artificial gravity can be achieved using…

In a hypothetical ring shaped satellite rotating in space, artificial gravity can be achieved using centripetal force. If the satellite has a radius $10 \mathrm{~m}$, then to achieve centripetal acceleration at a point on circumference as $10 \mathrm{~ms}^{-2}$, its angular speed is
  1. $1 \mathrm{rad} \mathrm{s}^{-1}$
  2. $10 \mathrm{rads}^{-1}$
  3. 1 revolution $\mathrm{s}^{-1}$
  4. 10 revolution $\mathrm{s}^{-1}$

Solution

Given, Radius, $r=10 \mathrm{~m}$ Centripetal acceleration, $a_6=10 \mathrm{~ms}^{-2}$ We know that, centripetal acceleration, $ \begin{aligned} a_\epsilon & =\omega^2 r \\ \Rightarrow \quad \omega & =\sqrt{\frac{a_\epsilon}{r}} \\ & =\sqrt{\frac{10}{10}}=1 \mathrm{rads}^{-1} \end{aligned} $

Asked in: AP EAMCET 2022 (06 Jul Shift 2)

Practice more Motion In Two Dimensions questions on Aicharya