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 fv, where v is its escape velocity from the 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 of the body from the surfaceof earth is `v=sqrt(2R)`
Escape velocity of the body from the platform is fv.
`:." potential energy "+" kinetic energy "=0`
`-(GMm)/(2R)+(1)/(2)mv^(2)=0 rArr v=sqrt((GM)/(R^(2))).R=sqrt(gR)=fv`
From the surface of the earth, `v_("escape")=sqrt(2gR)`
`:. fv=(v_("escape"))/(sqrt(2)) rArr f=(1)/(sqrt(2))`.