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A rocket of mass M is launched verticall...

A rocket of mass M is launched vertically from the surface of the earth with an initial speed `V= sqrt((gR)/(2))` . Assuming the radius of the earth to be R and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is `(R)/(X)` where X is:

Text Solution

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(3) `Delta K.E. = Delta U`
`rArr (1)/(2) MV^(2) = GM_(e)M ((1)/("R") - (1)/(R + h)))` …(i)
Also g = `(GM_(e))/(R^(2))` ….(ii)
On solving (i) and (ii) h = `("R")/(3)`
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