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