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Q.

Gravitational acceleration on the surface of a planet is 611g where g is the gravitational acceleration on the surface of the earth. The average mass density of the planet is 2/3 times that of the earth. If the escape speed on the surface of the earth is taken to be 11kms-1 , the escape speed on the surface of the planet in kms-1 will be

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a

3

b

6

c

9

d

12

answer is A.

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Detailed Solution

g=GMR2=G43πR3ρR2g∞ρR; R∞gρNow escape velocity, ve=2gRve∞gR; ve∞g×gρ∞g2ρveplanet =11kms−16121×32=3kms−1
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Gravitational acceleration on the surface of a planet is 611g where g is the gravitational acceleration on the surface of the earth. The average mass density of the planet is 2/3 times that of the earth. If the escape speed on the surface of the earth is taken to be 11kms-1 , the escape speed on the surface of the planet in kms-1 will be