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

Options

A. `(1)/(2)`
B. `sqrt(2)`
C. `(1)/(sqrt(2))`
D. `(1)/(3)`.

Answer

C

Explanation

Escape velocity from surface of earth is
`v=sqrt((2GM)/(R ))`
If v. is escape velocity from the platform then Kinetic energy + Gravitational potential energy = 0.
`(1)/(2)mv.^(2)+(-(GMm)/(2R))=0 rArr v.= sqrt((GM)/(R ))=fv`
`therefore f=(v.)/(v)=(1)/(sqrt(2))`.
Thus correct choice is (c ).