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Question

A projectile is fired vertically from the Earth with a velocity kve where ve is the escape velocity and k is a constant less than unity. The maximum height to which projectile rises, as measured from the centre of Earth, is

A
Rk
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B
Rk1
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C
R1k2
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D
R1+k2
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Solution

The correct option is D R1k2
Applying conservation of energy principle, we get
12mk2v2eGMmR=GMmr
12mk22GMRGMmR=GMmr
k2R1R=1r1r=1Rk2R
1r=1R(1k2)r=R1k2

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