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 ..........

The earth is assumed to be a sphere of radius R. A platform is arrange

1.	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 ..........
Answer» `1/sqrt2` `1/3` `1/2` `sqrt2` Solution :`implies` Potential energy at HEIGHT `R = - (GMM)/(2R)` If a body of MASS m isprojected 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`