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Question

A rocket is launched normal to the surface of the earth, away from the sun, along the line joining the sun and the earth. The sun is 3×105 times heavier than the earth and is at a distance 2.5×104 times larger than the radius of the earth. The escape velocity from earths gravitational field is Vc=11.2kms1 . The minimum initial (Vc) required for the rocket to be able to leave the sun-earth system is closest to (Ignore the rotation and revolution of the earth and the presence of any other planet)


A
(Vc)=22kms1
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B
(Vc)=42kms1
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C
(Vc)=62kms1
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D
(Vc)=72kms1
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Solution

The correct option is B (Vc)=42kms1
12mV2eGMemReGMem×3×1052.5×104Re=0
Ve22=GMmRe[1+3×1052.5×104]
Ve=13(2GMe)Re=13×11.242
The minimum initial Vs=42km/s.

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