A spherical uniform planet is rotating about its axis. The velocity of a point on its equator is 7 . 5 km s - 1 . 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. What is the escape velocity (in km s - 1 ) of a particle on the planet from the pole of the planet?

Question

A spherical uniform planet is rotating about its axis. The velocity of a point on its equator is 7 . 5 km s - 1 . 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. What is the escape velocity (in km s - 1 ) of a particle on the planet from the pole of the planet?,

MARKS App · 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 V e = 15 km s - 1

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