Gravitational acceleration on the surface of the planet is $$611g$$, where g is the acceleration due to gravity on the surface of earth. The average mass density of the planet is $$2/3$$ time that of the earth. If the escape speed on the surface of the earth is taken to be $$11$$ $$kms-1$$, then find the escape speed on the surface of the planet (in$$ $$kms-1).

Question

Gravitational acceleration on the surface of the planet is $$611g$$, where g is the acceleration due to gravity on the surface of earth. The average mass density of the planet is $$2/3$$ time that of the earth. If the escape speed on the surface of the earth is taken to be $$11$$ $$kms-1$$, then find the escape speed on the surface of the planet (in$$ $$kms-1).

Infinity Learn · Accepted Answer

We know that, $$g=GMR2=43$$$$π$$GRρ⇒g α ρR∴$$gpge=Rp$$ρpReρe also $$ve=2gR$$∴$$vepvee=gpRpgeRe=gpge$$⋅gpρegeρ$$p=gpge$$ρeρ$$p=61132=311$$∴ $$vrp=311vee=311(11)=3kms$$−$$1$$

Motion of planets and satellites

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Motion of planets and satellites

Remember concepts with our Masterclasses.

We know that, g=GMR2=43πGRρ⇒g α ρR∴gpge=RpρpReρe also ve=2gR∴vepvee=gpRpgeRe=gpge⋅gpρegeρp=gpgeρeρp=61132=311∴ vrp=311vee=311(11)=3kms−1

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