Gravitational acceleration on the surface of the planet is $$811g$$, where g is the acceleration due to gravity on the surface of earth. The average mass density of the planet is $$2$$ times 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 $$811g$$, where g is the acceleration due to gravity on the surface of earth. The average mass density of the planet is $$2$$ times 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, $$g=GMR2=43$$$$π$$GMρ∴$$gpge=Rp$$ρpReρe also $$ve=2gR$$∴$$vepvee=gpRpgeRe=gpge$$⋅gpρegeρ$$p=gpge$$ρeρ$$p=8112=411$$∴ $$vrp=411vee=411(11)=4kms$$−$$1$$

Motion of planets and satellites

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Motion of planets and satellites

Remember concepts with our Masterclasses.

We know that, g=GMR2=43πGMρ∴gpge=RpρpReρe also ve=2gR∴vepvee=gpRpgeRe=gpge⋅gpρegeρp=gpgeρeρp=8112=411∴ vrp=411vee=411(11)=4kms−1

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