The cosmonauts who landed at the pole of a planet found that the force of gravity there is \( 0....

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The cosmonauts who landed at the pole of a planet found that the force of gravity there is \( 0.01 \) of that on the Earth, while the duration of the day on the planet is the same as that on the Earth. It turned out besides that the force of gravity on the equator is zero.
Determine the radius \( R \) of the planet.
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