An object of mass m is raised up to a small height h above the earth's surface. If the acceleration due to gravity on the earth's surface is g, prove that the weight of the object will decreases by `(2mgh)/R` with respect to that on the earth's surface . R =radius of the earth.

Explanation

Acceleration due to gravity at a small height h above the earth.s surface is given by
`g^.=g(1-(2h)/R)`.
Hence, weight at that height,
`mg^.=mg(1-(2h)/R)=mg-(2mgh)/R`
or, `mg-mg^.=(2mgh)/R`
so, the decrease in weight with respect to that on the earth.s surface `=(2mgh)/R`.