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Question

A projectile is fired from the surface of earth of radius R with a velocity kve (where ve is the escape velocity from surface of earth and k<1) Neglecting air resistance, the maximum height of rise from the centre of earth is

A
Rk21
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B
k2R
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C
R1k2
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D
kR
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Solution

The correct option is D R1k2
At maximum height h, KE of the projectile will be zero.
Using conservation of energy, KEi+PEi=KEf+PEf
or 12m(kve)2GMmR=0GMmh

or 12k2(2gR)GMR+GMh=0 where escape velocity, ve=2gR

or gRk2gR+gR2/h=0 where g=GMR2

or k21+R/h=0h=R1k2

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