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The earth is assumed to be a sphere of r...

The earth is assumed to be a sphere of raduis `R`. A plateform is arranged at a height `R` from the surface of the `fv_(e)`, where `v_(e)` is its escape velocity form the surface of the earth. The value of `f` is

A

`1//2`

B

`sqrt(2)`

C

`1//sqrt(2)`

D

`1//3`

Text Solution

Verified by Experts

The correct Answer is:
C
As `f upsilon` is the escape velocity of the body from the platform, then using the law of conservation of total energy
or `-(GM m)/((R + R)) + (1)/(2)m(f upsilon)^(2) = 0`
or `f upsilon = sqrt((GM)/(R )) = sqrt((g R^(2))/(R )) = sqrt(g R)`.
The value of escape velocity from the surface of
earth `upsilon = sqrt(2g R)` or `sqrt(g R) = upsilon//sqrt(2)`
`:. f upsilon = upsilon//sqrt(2)` or `f = 1//sqrt(2)`
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