Q.

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

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a

VP=1.5VE

b

VP=2VE

c

VE=3VP

d

VE=1.5VP

answer is B.

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Detailed Solution

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