Q1) [30 marks, 5 for each] Consider a spherical planet with the mean density p, rotating at angular velocity 0. a) For w

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Q1 30 Marks 5 For Each Consider A Spherical Planet With The Mean Density P Rotating At Angular Velocity 0 A For W 1 (78.82 KiB) Viewed 28 times

Q1) [30 marks, 5 for each] Consider a spherical planet with the mean density p, rotating at angular velocity 0. a) For what critical value of o, say @erit, will equatorial gravitational acceleration vanish for objects on the planet's surface? b) What is the value of Ocrit for the Earth? c) By what factor does this critical angular velocity exceed the angular velocity of the Earth's rotation? d) What would be the value of f, the flattening of the Earth, when o = @crit? e) What would the ratio of the polar to equatorial radii be when w = @crit? f) Show that for 0 = 0crit, the corresponding angular momentum is Lerin = 0.32G*Mp where M is the planet's mass. Many planetary and asteroidal angular momenta follow a law of this form with a numerical constant of 0.07