A spherical uniform planet is rotating about its axis. The velocity of a point on its equator is V . Due to the rotation of the planet about its axis the acceleration due to gravity g at equator is 1

Question

A spherical uniform planet is rotating about its axis. The velocity of a point on its equator is V . Due to the rotation of the planet about its axis the acceleration due to gravity g at equator is 1 2 of g at poles. The escape velocity of a particle on the planet in terms of V from the pole of the planet is

TestHub · Accepted Answer

g e = g p - R ω 2 ⇒ g 2 = g - R ω 2 R ω 2 = g 2 ⇒ R 2 ω 2 = g R 2 ⇒ V 2 = g R 2 ...(1) The escape velocity, V e = 2 g R ...(2) From (1) and (2) V e = 2 × 2 V 2 ⇒ V e = 2 V

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