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A particle is projected vertically upwar...

A particle is projected vertically upwards with a velocity `sqrt(gR)`, where `R` denotes the radius of the earth and `g` the acceleration due to gravity on the surface of the earth. Then the maximum height ascended by the particle is

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The correct Answer is:
A
Let the object of mass m projected with speed
`u=sqrt(gR)` reach a height ‘h’ above surface of earth.
Then from conservation of energy, `1/2m u^2-(GMm)/R=-(GMm)/(R+h)`
`rArr u^2=gR=(GM)/R`
`rArr 1/2 (GMm)/R-(GMm)/R =-(GMm)/(R+h)` or h=R
`therefore` n=1
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