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A particle is projected upward from the ...

A particle is projected upward from the surface of the earth (radius) with a K.E. Equal to half the minimum value needed for it to escape. To which height, does it rise above the surface of earth?

Text Solution

Verified by Experts

For the particle to escape, K.E = P.E
`1/2 mV_(e)^(2) = (GMm)/(R + h)`
But supplied K.E. = 1/2 xx 1/2 m V_(e)^(2) = (GMm)/(2R)`
`Suppose the particle rises rises to a height h, then
`1/2 xx 1/2 mV_(e)^(2) = (GMm)/(R+h)`
`(GMm)/(R + h) = (GMm)/(2R)`
`h = R` .
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