A spherical planet has mass \( M \) and radius \( R \). The planet may be assumed to be isolated in space and to have its mass concentrated at its centre. The planet spins on its axis with angular speed \( \omega \).A small object of mass \( m \) rests on the equator of the planet. The surface of the planet exerts a normal reaction force on the mass.
State formulae, in terms of \( M, m, \mathrm{R} \) and \( \omega \) for \( (i) \) the gravitational force between the planet and the object, (ii) the centripetal force required for circular motion of the small mass and (iii) the normal reaction exerted by the planet on the mass.
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