The earth is assumed to be a sphere of radius R. A platform is arranged at a height R from the surface of the earth. The escape velocity of a body from this platform is fu, where v is its escape velocity from the surface of the earth the value of f is .......... 

Options

A. `1/sqrt2`
B. `1/3`
C. `1/2`
D. `sqrt2`

Answer

A

Explanation

`implies` Potential energy at height `R = - (GMm)/(2R)`
If a body of mass m is projected at height R from the surface of earth with the velocity `v_e` so that it goes beyond the earth.s gravitational field and escape from earth then ,
`1/2 mv_e^2 =(GM)/(2R) .m`
`:. v_e = sqrt((GM)/R) " or " v_e = sqrt(gR)`
Now `,v = sqrt(2gR) ` for `v = sqrt2 v_e ` or `v_e =1/sqrt2 v`
`:. f =1/sqrt 2`