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