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Question

From a planet of mass 16M and radius 4R, we wish to send an object to its moon of mass M and radius R. Distance between centres of planet and moon is 10R. Minimum speed at which object should be projected from the surface of planet so that it reaches moon is (Assume that the planet and the moon are at rest)

A
10GM3R
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B
8GMR
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C
7GM3R
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D
9GM2R
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Solution

The correct option is A 10GM3R

The object has to at least reach the point where the force on it due to the planet and the moon cancels out and becomes zero.
Say, the distance between the planet and that point is x1 and the distance between the moon and that point is x2. So,
G16Mmx21=GMmx22
x1=4x2
And,
x1+x2=10R
x1=8R and x2=2R

Lets conserve the initial energy and the final energy at that point.

12mV2G16Mm4RGMm(10R4R)=G16Mm8RGMm2R
V=10GM3R

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