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.
(i) Explain why the normal reaction on the mass will have different values at the equator and at the poles. (ii) The radius of the planet is \( 6.4 \times 10^{6} \mathrm{~m} \). It completes one revolution in \( 8.6 \times 10^{4} \mathrm{~s} \).Calculate the magnitude of the centripetal acceleration at the equator and one of the poles.
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