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The radius of a planet is twice the radius of earth. Both have almost equal average mass-densities. $V_{P} a n d V_{E}$ are escape velocities of the planet and the earth, respectively, then

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VP=1.5VE

VP=2VE

VE=3VP

VE=1.5VP

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detailed solution

Correct option is B

Here, RP=2RE,ρE=ρP Escape velocity of the earth, VE=2GMERE=2GRE43πRE3ρE=RE83πGρE ....(i) Escape velocity of planet, VP=2GMPRP=2GRP43πRP3ρP=RP83πGρP .......(ii) Divide (i) by (ii), we get VEVP=RERPρEρP VEVP=RE2REρEρE=12 or VP=2VE

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The radius of a planet is twice the radius of earth. Both have almost equal average mass-densities. VP and VE are escape velocities of the planet and the earth, respectively, then

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

The radius of a planet is twice the radius of earth. Both have almost equal average mass-densities. $V_{P} a n d V_{E}$ are escape velocities of the planet and the earth, respectively, then