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Q.

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).

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Detailed Solution

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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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).