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A particle is projected vertically upwar...

A particle is projected vertically upwards from the surface of earth (radius R) with a kinetic energy equal to half of the minimum value needed for it to escape. The height to which it rises above the surface of earth is

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The correct Answer is:
NA
Applying energy conservation
Total energy at `A =` Total energy at `B`
`1/2mv^(2)=(-(GMm)/r)=-(GMm)/(R+h)` ………..i
Escape velocity`=V_(e)=sqrt((2GM)/R)`
Therefore kinetic energy required for escape velocity is
`1/2mv_(e)^(2)=(GMm)/(2R)`
From eqn i and ii
`(GMm)/(2R)-(GMm)/R=-(GMm)/(R+h)`
`implies -1/(2R)=-1/(R+h)impliesR+h=2R`
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